LCOV - code coverage report
Current view: top level - src/include/lib - radixtree.h (source / functions) Hit Total Coverage
Test: PostgreSQL 18devel Lines: 690 767 90.0 %
Date: 2024-07-27 00:11:07 Functions: 139 144 96.5 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : /*-------------------------------------------------------------------------
       2             :  *
       3             :  * radixtree.h
       4             :  *      Template for adaptive radix tree.
       5             :  *
       6             :  * A template to generate an "adaptive radix tree", specialized for value
       7             :  * types and for local/shared memory.
       8             :  *
       9             :  * The concept originates from the paper "The Adaptive Radix Tree: ARTful
      10             :  * Indexing for Main-Memory Databases" by Viktor Leis, Alfons Kemper,
      11             :  * and Thomas Neumann, 2013.
      12             :  *
      13             :  * Radix trees have some advantages over hash tables:
      14             :  * - The keys are logically ordered, allowing efficient sorted iteration
      15             :  *   and range queries
      16             :  * - Operations using keys that are lexicographically close together
      17             :  *   will have favorable memory locality
      18             :  * - Memory use grows gradually rather than by doubling
      19             :  * - The key does not need to be stored with the value, since the key
      20             :  *   is implicitly contained in the path to the value
      21             :  *
      22             :  * Some disadvantages are:
      23             :  * - Point queries (along with insertion and deletion) are slower than
      24             :  *   a linear probing hash table as in simplehash.h
      25             :  * - Memory usage varies by key distribution, so is difficult to predict
      26             :  *
      27             :  * A classic radix tree consists of nodes, each containing an array of
      28             :  * pointers to child nodes.  The size of the array is determined by the
      29             :  * "span" of the tree, which is the number of bits of the key used to
      30             :  * index into the array.  For example, with a span of 6, a "chunk"
      31             :  * of 6 bits is extracted from the key at each node traversal, and
      32             :  * the arrays thus have a "fanout" of 2^6 or 64 entries.  A large span
      33             :  * allows a shorter tree, but requires larger arrays that may be mostly
      34             :  * wasted space.
      35             :  *
      36             :  * The key idea of the adaptive radix tree is to choose different
      37             :  * data structures based on the number of child nodes. A node will
      38             :  * start out small when it is first populated, and when it is full,
      39             :  * it is replaced by the next larger size. Conversely, when a node
      40             :  * becomes mostly empty, it is replaced by the next smaller node. The
      41             :  * bulk of the code complexity in this module stems from this dynamic
      42             :  * switching. One mitigating factor is using a span of 8, since bytes
      43             :  * are directly addressable.
      44             :  *
      45             :  * The ART paper mentions three ways to implement leaves:
      46             :  *
      47             :  * "- Single-value leaves: The values are stored using an addi-
      48             :  *  tional leaf node type which stores one value.
      49             :  *  - Multi-value leaves: The values are stored in one of four
      50             :  *  different leaf node types, which mirror the structure of
      51             :  *  inner nodes, but contain values instead of pointers.
      52             :  *  - Combined pointer/value slots: If values fit into point-
      53             :  *  ers, no separate node types are necessary. Instead, each
      54             :  *  pointer storage location in an inner node can either
      55             :  *  store a pointer or a value."
      56             :  *
      57             :  * We use a form of "combined pointer/value slots", as recommended. Values
      58             :  * of size (if fixed at compile time) equal or smaller than the platform's
      59             :  * pointer type are stored in the child slots of the last level node,
      60             :  * while larger values are the same as "single-value" leaves above. This
      61             :  * offers flexibility and efficiency. Variable-length types are currently
      62             :  * treated as single-value leaves for simplicity, but future work may
      63             :  * allow those to be stored in the child pointer arrays, when they're
      64             :  * small enough.
      65             :  *
      66             :  * There are two other techniques described in the paper that are not
      67             :  * implemented here:
      68             :  * - path compression "...removes all inner nodes that have only a single child."
      69             :  * - lazy path expansion "...inner nodes are only created if they are required
      70             :  *   to distinguish at least two leaf nodes."
      71             :  *
      72             :  * We do have a form of "poor man's path compression", however, enabled by
      73             :  * only supporting unsigned integer keys (for now assumed to be 64-bit):
      74             :  * A tree doesn't contain paths where the highest bytes of all keys are
      75             :  * zero. That way, the tree's height adapts to the distribution of keys.
      76             :  *
      77             :  * To handle concurrency, we use a single reader-writer lock for the
      78             :  * radix tree. If concurrent write operations are possible, the tree
      79             :  * must be exclusively locked during write operations such as RT_SET()
      80             :  * and RT_DELETE(), and share locked during read operations such as
      81             :  * RT_FIND() and RT_BEGIN_ITERATE().
      82             :  *
      83             :  * TODO: The current locking mechanism is not optimized for high
      84             :  * concurrency with mixed read-write workloads. In the future it might
      85             :  * be worthwhile to replace it with the Optimistic Lock Coupling or
      86             :  * ROWEX mentioned in the paper "The ART of Practical Synchronization"
      87             :  * by the same authors as the ART paper, 2016.
      88             :  *
      89             :  * To generate a radix tree and associated functions for a use case
      90             :  * several macros have to be #define'ed before this file is included.
      91             :  * Including the file #undef's all those, so a new radix tree can be
      92             :  * generated afterwards.
      93             :  *
      94             :  * The relevant parameters are:
      95             :  * - RT_PREFIX - prefix for all symbol names generated. A prefix of "foo"
      96             :  *   will result in radix tree type "foo_radix_tree" and functions like
      97             :  *   "foo_create"/"foo_free" and so forth.
      98             :  * - RT_DECLARE - if defined function prototypes and type declarations are
      99             :  *   generated
     100             :  * - RT_DEFINE - if defined function definitions are generated
     101             :  * - RT_SCOPE - in which scope (e.g. extern, static inline) do function
     102             :  *   declarations reside
     103             :  * - RT_VALUE_TYPE - the type of the value.
     104             :  * - RT_VARLEN_VALUE_SIZE() - for variable length values, an expression
     105             :  *   involving a pointer to the value type, to calculate size.
     106             :  *     NOTE: implies that the value is in fact variable-length,
     107             :  *     so do not set for fixed-length values.
     108             :  * - RT_RUNTIME_EMBEDDABLE_VALUE - for variable length values, allows
     109             :  *   storing the value in a child pointer slot, rather than as a single-
     110             :  *   value leaf, if small enough. This requires that the value, when
     111             :  *   read as a child pointer, can be tagged in the lowest bit.
     112             :  *
     113             :  * Optional parameters:
     114             :  * - RT_SHMEM - if defined, the radix tree is created in the DSA area
     115             :  *   so that multiple processes can access it simultaneously.
     116             :  * - RT_DEBUG - if defined add stats tracking and debugging functions
     117             :  *
     118             :  * Interface
     119             :  * ---------
     120             :  *
     121             :  * RT_CREATE        - Create a new, empty radix tree
     122             :  * RT_FREE          - Free the radix tree
     123             :  * RT_FIND          - Lookup the value for a given key
     124             :  * RT_SET           - Set a key-value pair
     125             :  * RT_BEGIN_ITERATE - Begin iterating through all key-value pairs
     126             :  * RT_ITERATE_NEXT  - Return next key-value pair, if any
     127             :  * RT_END_ITERATE   - End iteration
     128             :  * RT_MEMORY_USAGE  - Get the memory as measured by space in memory context blocks
     129             :  *
     130             :  * Interface for Shared Memory
     131             :  * ---------
     132             :  *
     133             :  * RT_ATTACH        - Attach to the radix tree
     134             :  * RT_DETACH        - Detach from the radix tree
     135             :  * RT_LOCK_EXCLUSIVE - Lock the radix tree in exclusive mode
     136             :  * RT_LOCK_SHARE    - Lock the radix tree in share mode
     137             :  * RT_UNLOCK        - Unlock the radix tree
     138             :  * RT_GET_HANDLE    - Return the handle of the radix tree
     139             :  *
     140             :  * Optional Interface
     141             :  * ---------
     142             :  *
     143             :  * RT_DELETE        - Delete a key-value pair. Declared/defined if RT_USE_DELETE is defined
     144             :  *
     145             :  *
     146             :  * Copyright (c) 2024, PostgreSQL Global Development Group
     147             :  *
     148             :  * IDENTIFICATION
     149             :  *    src/include/lib/radixtree.h
     150             :  *
     151             :  *-------------------------------------------------------------------------
     152             :  */
     153             : 
     154             : #include "postgres.h"
     155             : 
     156             : #include "nodes/bitmapset.h"
     157             : #include "port/pg_bitutils.h"
     158             : #include "port/simd.h"
     159             : #include "utils/dsa.h"
     160             : #include "utils/memutils.h"
     161             : 
     162             : /* helpers */
     163             : #define RT_MAKE_PREFIX(a) CppConcat(a,_)
     164             : #define RT_MAKE_NAME(name) RT_MAKE_NAME_(RT_MAKE_PREFIX(RT_PREFIX),name)
     165             : #define RT_MAKE_NAME_(a,b) CppConcat(a,b)
     166             : /*
     167             :  * stringify a macro constant, from https://gcc.gnu.org/onlinedocs/cpp/Stringizing.html
     168             :  */
     169             : #define RT_STR(s) RT_STR_(s)
     170             : #define RT_STR_(s) #s
     171             : 
     172             : /* function declarations */
     173             : #define RT_CREATE RT_MAKE_NAME(create)
     174             : #define RT_FREE RT_MAKE_NAME(free)
     175             : #define RT_FIND RT_MAKE_NAME(find)
     176             : #ifdef RT_SHMEM
     177             : #define RT_ATTACH RT_MAKE_NAME(attach)
     178             : #define RT_DETACH RT_MAKE_NAME(detach)
     179             : #define RT_GET_HANDLE RT_MAKE_NAME(get_handle)
     180             : #define RT_LOCK_EXCLUSIVE RT_MAKE_NAME(lock_exclusive)
     181             : #define RT_LOCK_SHARE RT_MAKE_NAME(lock_share)
     182             : #define RT_UNLOCK RT_MAKE_NAME(unlock)
     183             : #endif
     184             : #define RT_SET RT_MAKE_NAME(set)
     185             : #define RT_BEGIN_ITERATE RT_MAKE_NAME(begin_iterate)
     186             : #define RT_ITERATE_NEXT RT_MAKE_NAME(iterate_next)
     187             : #define RT_END_ITERATE RT_MAKE_NAME(end_iterate)
     188             : #ifdef RT_USE_DELETE
     189             : #define RT_DELETE RT_MAKE_NAME(delete)
     190             : #endif
     191             : #define RT_MEMORY_USAGE RT_MAKE_NAME(memory_usage)
     192             : #define RT_DUMP_NODE RT_MAKE_NAME(dump_node)
     193             : #define RT_STATS RT_MAKE_NAME(stats)
     194             : 
     195             : /* internal helper functions (no externally visible prototypes) */
     196             : #define RT_CHILDPTR_IS_VALUE RT_MAKE_NAME(childptr_is_value)
     197             : #define RT_VALUE_IS_EMBEDDABLE RT_MAKE_NAME(value_is_embeddable)
     198             : #define RT_GET_SLOT_RECURSIVE RT_MAKE_NAME(get_slot_recursive)
     199             : #define RT_DELETE_RECURSIVE RT_MAKE_NAME(delete_recursive)
     200             : #define RT_ALLOC_NODE RT_MAKE_NAME(alloc_node)
     201             : #define RT_ALLOC_LEAF RT_MAKE_NAME(alloc_leaf)
     202             : #define RT_FREE_NODE RT_MAKE_NAME(free_node)
     203             : #define RT_FREE_LEAF RT_MAKE_NAME(free_leaf)
     204             : #define RT_FREE_RECURSE RT_MAKE_NAME(free_recurse)
     205             : #define RT_EXTEND_UP RT_MAKE_NAME(extend_up)
     206             : #define RT_EXTEND_DOWN RT_MAKE_NAME(extend_down)
     207             : #define RT_COPY_COMMON RT_MAKE_NAME(copy_common)
     208             : #define RT_PTR_SET_LOCAL RT_MAKE_NAME(ptr_set_local)
     209             : #define RT_NODE_16_SEARCH_EQ RT_MAKE_NAME(node_16_search_eq)
     210             : #define RT_NODE_4_GET_INSERTPOS RT_MAKE_NAME(node_4_get_insertpos)
     211             : #define RT_NODE_16_GET_INSERTPOS RT_MAKE_NAME(node_16_get_insertpos)
     212             : #define RT_SHIFT_ARRAYS_FOR_INSERT RT_MAKE_NAME(shift_arrays_for_insert)
     213             : #define RT_SHIFT_ARRAYS_AND_DELETE RT_MAKE_NAME(shift_arrays_and_delete)
     214             : #define RT_COPY_ARRAYS_FOR_INSERT RT_MAKE_NAME(copy_arrays_for_insert)
     215             : #define RT_COPY_ARRAYS_AND_DELETE RT_MAKE_NAME(copy_arrays_and_delete)
     216             : #define RT_NODE_48_IS_CHUNK_USED RT_MAKE_NAME(node_48_is_chunk_used)
     217             : #define RT_NODE_48_GET_CHILD RT_MAKE_NAME(node_48_get_child)
     218             : #define RT_NODE_256_IS_CHUNK_USED RT_MAKE_NAME(node_256_is_chunk_used)
     219             : #define RT_NODE_256_GET_CHILD RT_MAKE_NAME(node_256_get_child)
     220             : #define RT_KEY_GET_SHIFT RT_MAKE_NAME(key_get_shift)
     221             : #define RT_SHIFT_GET_MAX_VAL RT_MAKE_NAME(shift_get_max_val)
     222             : #define RT_NODE_SEARCH RT_MAKE_NAME(node_search)
     223             : #define RT_NODE_DELETE RT_MAKE_NAME(node_delete)
     224             : #define RT_NODE_INSERT RT_MAKE_NAME(node_insert)
     225             : #define RT_ADD_CHILD_4 RT_MAKE_NAME(add_child_4)
     226             : #define RT_ADD_CHILD_16 RT_MAKE_NAME(add_child_16)
     227             : #define RT_ADD_CHILD_48 RT_MAKE_NAME(add_child_48)
     228             : #define RT_ADD_CHILD_256 RT_MAKE_NAME(add_child_256)
     229             : #define RT_GROW_NODE_4 RT_MAKE_NAME(grow_node_4)
     230             : #define RT_GROW_NODE_16 RT_MAKE_NAME(grow_node_16)
     231             : #define RT_GROW_NODE_48 RT_MAKE_NAME(grow_node_48)
     232             : #define RT_REMOVE_CHILD_4 RT_MAKE_NAME(remove_child_4)
     233             : #define RT_REMOVE_CHILD_16 RT_MAKE_NAME(remove_child_16)
     234             : #define RT_REMOVE_CHILD_48 RT_MAKE_NAME(remove_child_48)
     235             : #define RT_REMOVE_CHILD_256 RT_MAKE_NAME(remove_child_256)
     236             : #define RT_SHRINK_NODE_16 RT_MAKE_NAME(shrink_child_16)
     237             : #define RT_SHRINK_NODE_48 RT_MAKE_NAME(shrink_child_48)
     238             : #define RT_SHRINK_NODE_256 RT_MAKE_NAME(shrink_child_256)
     239             : #define RT_NODE_ITERATE_NEXT RT_MAKE_NAME(node_iterate_next)
     240             : #define RT_VERIFY_NODE RT_MAKE_NAME(verify_node)
     241             : 
     242             : /* type declarations */
     243             : #define RT_RADIX_TREE RT_MAKE_NAME(radix_tree)
     244             : #define RT_RADIX_TREE_CONTROL RT_MAKE_NAME(radix_tree_control)
     245             : #define RT_ITER RT_MAKE_NAME(iter)
     246             : #ifdef RT_SHMEM
     247             : #define RT_HANDLE RT_MAKE_NAME(handle)
     248             : #endif
     249             : #define RT_NODE RT_MAKE_NAME(node)
     250             : #define RT_CHILD_PTR RT_MAKE_NAME(child_ptr)
     251             : #define RT_NODE_ITER RT_MAKE_NAME(node_iter)
     252             : #define RT_NODE_4 RT_MAKE_NAME(node_4)
     253             : #define RT_NODE_16 RT_MAKE_NAME(node_16)
     254             : #define RT_NODE_48 RT_MAKE_NAME(node_48)
     255             : #define RT_NODE_256 RT_MAKE_NAME(node_256)
     256             : #define RT_SIZE_CLASS RT_MAKE_NAME(size_class)
     257             : #define RT_SIZE_CLASS_ELEM RT_MAKE_NAME(size_class_elem)
     258             : #define RT_SIZE_CLASS_INFO RT_MAKE_NAME(size_class_info)
     259             : #define RT_CLASS_4 RT_MAKE_NAME(class_4)
     260             : #define RT_CLASS_16_LO RT_MAKE_NAME(class_32_min)
     261             : #define RT_CLASS_16_HI RT_MAKE_NAME(class_32_max)
     262             : #define RT_CLASS_48 RT_MAKE_NAME(class_48)
     263             : #define RT_CLASS_256 RT_MAKE_NAME(class_256)
     264             : 
     265             : /* generate forward declarations necessary to use the radix tree */
     266             : #ifdef RT_DECLARE
     267             : 
     268             : typedef struct RT_RADIX_TREE RT_RADIX_TREE;
     269             : typedef struct RT_ITER RT_ITER;
     270             : 
     271             : #ifdef RT_SHMEM
     272             : typedef dsa_pointer RT_HANDLE;
     273             : #endif
     274             : 
     275             : #ifdef RT_SHMEM
     276             : RT_SCOPE    RT_RADIX_TREE *RT_CREATE(MemoryContext ctx, dsa_area *dsa, int tranche_id);
     277             : RT_SCOPE    RT_RADIX_TREE *RT_ATTACH(dsa_area *dsa, dsa_pointer dp);
     278             : RT_SCOPE void RT_DETACH(RT_RADIX_TREE * tree);
     279             : RT_SCOPE    RT_HANDLE RT_GET_HANDLE(RT_RADIX_TREE * tree);
     280             : RT_SCOPE void RT_LOCK_EXCLUSIVE(RT_RADIX_TREE * tree);
     281             : RT_SCOPE void RT_LOCK_SHARE(RT_RADIX_TREE * tree);
     282             : RT_SCOPE void RT_UNLOCK(RT_RADIX_TREE * tree);
     283             : #else
     284             : RT_SCOPE    RT_RADIX_TREE *RT_CREATE(MemoryContext ctx);
     285             : #endif
     286             : RT_SCOPE void RT_FREE(RT_RADIX_TREE * tree);
     287             : 
     288             : RT_SCOPE    RT_VALUE_TYPE *RT_FIND(RT_RADIX_TREE * tree, uint64 key);
     289             : RT_SCOPE bool RT_SET(RT_RADIX_TREE * tree, uint64 key, RT_VALUE_TYPE * value_p);
     290             : 
     291             : #ifdef RT_USE_DELETE
     292             : RT_SCOPE bool RT_DELETE(RT_RADIX_TREE * tree, uint64 key);
     293             : #endif
     294             : 
     295             : RT_SCOPE    RT_ITER *RT_BEGIN_ITERATE(RT_RADIX_TREE * tree);
     296             : RT_SCOPE    RT_VALUE_TYPE *RT_ITERATE_NEXT(RT_ITER * iter, uint64 *key_p);
     297             : RT_SCOPE void RT_END_ITERATE(RT_ITER * iter);
     298             : 
     299             : RT_SCOPE uint64 RT_MEMORY_USAGE(RT_RADIX_TREE * tree);
     300             : 
     301             : #ifdef RT_DEBUG
     302             : RT_SCOPE void RT_STATS(RT_RADIX_TREE * tree);
     303             : #endif
     304             : 
     305             : #endif                          /* RT_DECLARE */
     306             : 
     307             : 
     308             : /* generate implementation of the radix tree */
     309             : #ifdef RT_DEFINE
     310             : 
     311             : /* The number of bits encoded in one tree level */
     312             : #define RT_SPAN BITS_PER_BYTE
     313             : 
     314             : /*
     315             :  * The number of possible partial keys, and thus the maximum number of
     316             :  * child pointers, for a node.
     317             :  */
     318             : #define RT_NODE_MAX_SLOTS (1 << RT_SPAN)
     319             : 
     320             : /* Mask for extracting a chunk from a key */
     321             : #define RT_CHUNK_MASK ((1 << RT_SPAN) - 1)
     322             : 
     323             : /* Maximum shift needed to extract a chunk from a key */
     324             : #define RT_MAX_SHIFT    RT_KEY_GET_SHIFT(UINT64_MAX)
     325             : 
     326             : /* Maximum level a tree can reach for a key */
     327             : #define RT_MAX_LEVEL    ((sizeof(uint64) * BITS_PER_BYTE) / RT_SPAN)
     328             : 
     329             : /* Get a chunk from the key */
     330             : #define RT_GET_KEY_CHUNK(key, shift) ((uint8) (((key) >> (shift)) & RT_CHUNK_MASK))
     331             : 
     332             : /* For accessing bitmaps */
     333             : #define RT_BM_IDX(x)    ((x) / BITS_PER_BITMAPWORD)
     334             : #define RT_BM_BIT(x)    ((x) % BITS_PER_BITMAPWORD)
     335             : 
     336             : /*
     337             :  * Node kinds
     338             :  *
     339             :  * The different node kinds are what make the tree "adaptive".
     340             :  *
     341             :  * Each node kind is associated with a different datatype and different
     342             :  * search/set/delete/iterate algorithms adapted for its size. The largest
     343             :  * kind, node256 is basically the same as a traditional radix tree,
     344             :  * and would be most wasteful of memory when sparsely populated. The
     345             :  * smaller nodes expend some additional CPU time to enable a smaller
     346             :  * memory footprint.
     347             :  *
     348             :  * NOTE: There are 4 node kinds, and this should never be increased,
     349             :  * for several reasons:
     350             :  * 1. With 5 or more kinds, gcc tends to use a jump table for switch
     351             :  *    statements.
     352             :  * 2. The 4 kinds can be represented with 2 bits, so we have the option
     353             :  *    in the future to tag the node pointer with the kind, even on
     354             :  *    platforms with 32-bit pointers. That would touch fewer cache lines
     355             :  *    during traversal and allow faster recovery from branch mispredicts.
     356             :  * 3. We can have multiple size classes per node kind.
     357             :  */
     358             : #define RT_NODE_KIND_4          0x00
     359             : #define RT_NODE_KIND_16         0x01
     360             : #define RT_NODE_KIND_48         0x02
     361             : #define RT_NODE_KIND_256        0x03
     362             : #define RT_NODE_KIND_COUNT      4
     363             : 
     364             : /*
     365             :  * Calculate the slab block size so that we can allocate at least 32 chunks
     366             :  * from the block.
     367             :  */
     368             : #define RT_SLAB_BLOCK_SIZE(size)    \
     369             :     Max(SLAB_DEFAULT_BLOCK_SIZE, pg_nextpower2_32(size * 32))
     370             : 
     371             : /* Common header for all nodes */
     372             : typedef struct RT_NODE
     373             : {
     374             :     /* Node kind, one per search/set algorithm */
     375             :     uint8       kind;
     376             : 
     377             :     /*
     378             :      * Max capacity for the current size class. Storing this in the node
     379             :      * enables multiple size classes per node kind. uint8 is sufficient for
     380             :      * all node kinds, because we only use this number to test if the node
     381             :      * needs to grow. Since node256 never needs to grow, we let this overflow
     382             :      * to zero.
     383             :      */
     384             :     uint8       fanout;
     385             : 
     386             :     /*
     387             :      * Number of children. uint8 is sufficient for all node kinds, because
     388             :      * nodes shrink when this number gets lower than some threshold. Since
     389             :      * node256 cannot possibly have zero children, we let the counter overflow
     390             :      * and we interpret zero as "256" for this node kind.
     391             :      */
     392             :     uint8       count;
     393             : }           RT_NODE;
     394             : 
     395             : 
     396             : /* pointer returned by allocation */
     397             : #ifdef RT_SHMEM
     398             : #define RT_PTR_ALLOC dsa_pointer
     399             : #define RT_INVALID_PTR_ALLOC InvalidDsaPointer
     400             : #define RT_PTR_ALLOC_IS_VALID(ptr) DsaPointerIsValid(ptr)
     401             : #else
     402             : #define RT_PTR_ALLOC RT_NODE *
     403             : #define RT_INVALID_PTR_ALLOC NULL
     404             : #define RT_PTR_ALLOC_IS_VALID(ptr) PointerIsValid(ptr)
     405             : #endif
     406             : 
     407             : /*
     408             :  * A convenience type used when we need to work with a DSA pointer as well
     409             :  * as its local pointer. For local memory, both members are the same, so
     410             :  * we use a union.
     411             :  */
     412             : #ifdef RT_SHMEM
     413             : typedef struct RT_CHILD_PTR
     414             : #else
     415             : typedef union RT_CHILD_PTR
     416             : #endif
     417             : {
     418             :     RT_PTR_ALLOC alloc;
     419             :     RT_NODE    *local;
     420             : }           RT_CHILD_PTR;
     421             : 
     422             : 
     423             : /*
     424             :  * Helper macros and functions for value storage.
     425             :  * We either embed values in the child slots of the last level
     426             :  * node or store pointers to values to the child slots,
     427             :  * depending on the value size.
     428             :  */
     429             : 
     430             : #ifdef RT_VARLEN_VALUE_SIZE
     431             : #define RT_GET_VALUE_SIZE(v) RT_VARLEN_VALUE_SIZE(v)
     432             : #else
     433             : #define RT_GET_VALUE_SIZE(v) sizeof(RT_VALUE_TYPE)
     434             : #endif
     435             : 
     436             : /*
     437             :  * Return true if the value can be stored in the child array
     438             :  * of the lowest-level node, false otherwise.
     439             :  */
     440             : static inline bool
     441      236468 : RT_VALUE_IS_EMBEDDABLE(RT_VALUE_TYPE * value_p)
     442             : {
     443             : #ifdef RT_VARLEN_VALUE_SIZE
     444             : 
     445             : #ifdef RT_RUNTIME_EMBEDDABLE_VALUE
     446       23400 :     return RT_GET_VALUE_SIZE(value_p) <= sizeof(RT_PTR_ALLOC);
     447             : #else
     448             :     return false;
     449             : #endif
     450             : 
     451             : #else
     452      213068 :     return RT_GET_VALUE_SIZE(value_p) <= sizeof(RT_PTR_ALLOC);
     453             : #endif
     454             : }
     455             : 
     456             : /*
     457             :  * Return true if the child pointer contains the value, false
     458             :  * if the child pointer is a leaf pointer.
     459             :  */
     460             : static inline bool
     461     8801232 : RT_CHILDPTR_IS_VALUE(RT_PTR_ALLOC child)
     462             : {
     463             : #ifdef RT_VARLEN_VALUE_SIZE
     464             : 
     465             : #ifdef RT_RUNTIME_EMBEDDABLE_VALUE
     466             :     /* check for pointer tag */
     467             : #ifdef RT_SHMEM
     468      790502 :     return child & 1;
     469             : #else
     470     7402120 :     return ((uintptr_t) child) & 1;
     471             : #endif
     472             : 
     473             : #else
     474             :     return false;
     475             : #endif
     476             : 
     477             : #else
     478      608610 :     return sizeof(RT_VALUE_TYPE) <= sizeof(RT_PTR_ALLOC);
     479             : #endif
     480             : }
     481             : 
     482             : /*
     483             :  * Symbols for maximum possible fanout are declared first as they are
     484             :  * required to declare each node kind. The declarations of other fanout
     485             :  * values are followed as they need the struct sizes of each node kind.
     486             :  */
     487             : 
     488             : /* max possible key chunks without struct padding */
     489             : #define RT_FANOUT_4_MAX (8 - sizeof(RT_NODE))
     490             : 
     491             : /* equal to two 128-bit SIMD registers, regardless of availability */
     492             : #define RT_FANOUT_16_MAX    32
     493             : 
     494             : /*
     495             :  * This also determines the number of bits necessary for the isset array,
     496             :  * so we need to be mindful of the size of bitmapword.  Since bitmapword
     497             :  * can be 64 bits, the only values that make sense here are 64 and 128.
     498             :  * The ART paper uses at most 64 for this node kind, and one advantage
     499             :  * for us is that "isset" is a single bitmapword on most platforms,
     500             :  * rather than an array, allowing the compiler to get rid of loops.
     501             :  */
     502             : #define RT_FANOUT_48_MAX 64
     503             : 
     504             : #define RT_FANOUT_256   RT_NODE_MAX_SLOTS
     505             : 
     506             : /*
     507             :  * Node structs, one for each "kind"
     508             :  */
     509             : 
     510             : /*
     511             :  * node4 and node16 use one array for key chunks and another
     512             :  * array of the same length for children. The keys and children
     513             :  * are stored at corresponding positions, sorted by chunk.
     514             :  */
     515             : 
     516             : typedef struct RT_NODE_4
     517             : {
     518             :     RT_NODE     base;
     519             : 
     520             :     uint8       chunks[RT_FANOUT_4_MAX];
     521             : 
     522             :     /* number of children depends on size class */
     523             :     RT_PTR_ALLOC children[FLEXIBLE_ARRAY_MEMBER];
     524             : }           RT_NODE_4;
     525             : 
     526             : typedef struct RT_NODE_16
     527             : {
     528             :     RT_NODE     base;
     529             : 
     530             :     uint8       chunks[RT_FANOUT_16_MAX];
     531             : 
     532             :     /* number of children depends on size class */
     533             :     RT_PTR_ALLOC children[FLEXIBLE_ARRAY_MEMBER];
     534             : }           RT_NODE_16;
     535             : 
     536             : /*
     537             :  * node48 uses a 256-element array indexed by key chunks. This array
     538             :  * stores indexes into a second array containing the children.
     539             :  */
     540             : typedef struct RT_NODE_48
     541             : {
     542             :     RT_NODE     base;
     543             : 
     544             :     /* bitmap to track which slots are in use */
     545             :     bitmapword  isset[RT_BM_IDX(RT_FANOUT_48_MAX)];
     546             : 
     547             :     /*
     548             :      * Lookup table for indexes into the children[] array. We make this the
     549             :      * last fixed-size member so that it's convenient to memset separately
     550             :      * from the previous members.
     551             :      */
     552             :     uint8       slot_idxs[RT_NODE_MAX_SLOTS];
     553             : 
     554             : /* Invalid index */
     555             : #define RT_INVALID_SLOT_IDX 0xFF
     556             : 
     557             :     /* number of children depends on size class */
     558             :     RT_PTR_ALLOC children[FLEXIBLE_ARRAY_MEMBER];
     559             : }           RT_NODE_48;
     560             : 
     561             : /*
     562             :  * node256 is the largest node type. This node has an array of
     563             :  * children directly indexed by chunk.  Unlike other node kinds,
     564             :  * its array size is by definition fixed.
     565             :  */
     566             : typedef struct RT_NODE_256
     567             : {
     568             :     RT_NODE     base;
     569             : 
     570             :     /* bitmap to track which slots are in use */
     571             :     bitmapword  isset[RT_BM_IDX(RT_FANOUT_256)];
     572             : 
     573             :     /* slots for 256 children */
     574             :     RT_PTR_ALLOC children[RT_FANOUT_256];
     575             : }           RT_NODE_256;
     576             : 
     577             : #if defined(RT_SHMEM)
     578             : /*
     579             :  * Make sure the all nodes (except for node256) fit neatly into a DSA
     580             :  * size class.  We assume the RT_FANOUT_4 is in the range where DSA size
     581             :  * classes increment by 8 (as of PG17 up to 64 bytes), so we just hard
     582             :  * code that one.
     583             :  */
     584             : 
     585             : #if SIZEOF_DSA_POINTER < 8
     586             : #define RT_FANOUT_16_LO ((96 - offsetof(RT_NODE_16, children)) / sizeof(RT_PTR_ALLOC))
     587             : #define RT_FANOUT_16_HI Min(RT_FANOUT_16_MAX, (160 - offsetof(RT_NODE_16, children)) / sizeof(RT_PTR_ALLOC))
     588             : #define RT_FANOUT_48    Min(RT_FANOUT_48_MAX, (512 - offsetof(RT_NODE_48, children)) / sizeof(RT_PTR_ALLOC))
     589             : #else
     590             : #define RT_FANOUT_16_LO ((160 - offsetof(RT_NODE_16, children)) / sizeof(RT_PTR_ALLOC))
     591             : #define RT_FANOUT_16_HI Min(RT_FANOUT_16_MAX, (320 - offsetof(RT_NODE_16, children)) / sizeof(RT_PTR_ALLOC))
     592             : #define RT_FANOUT_48    Min(RT_FANOUT_48_MAX, (768 - offsetof(RT_NODE_48, children)) / sizeof(RT_PTR_ALLOC))
     593             : #endif                          /* SIZEOF_DSA_POINTER < 8 */
     594             : 
     595             : #else                           /* ! RT_SHMEM */
     596             : 
     597             : /* doesn't really matter, but may as well use the namesake */
     598             : #define RT_FANOUT_16_LO 16
     599             : /* use maximum possible */
     600             : #define RT_FANOUT_16_HI RT_FANOUT_16_MAX
     601             : #define RT_FANOUT_48    RT_FANOUT_48_MAX
     602             : 
     603             : #endif                          /* RT_SHMEM */
     604             : 
     605             : /*
     606             :  * To save memory in trees with sparse keys, it would make sense to have two
     607             :  * size classes for the smallest kind (perhaps a high class of 5 and a low class
     608             :  * of 2), but it would be more effective to utilize lazy expansion and
     609             :  * path compression.
     610             :  */
     611             : #define RT_FANOUT_4     4
     612             : 
     613             : StaticAssertDecl(RT_FANOUT_4 <= RT_FANOUT_4_MAX, "watch struct padding");
     614             : StaticAssertDecl(RT_FANOUT_16_LO < RT_FANOUT_16_HI, "LO subclass bigger than HI");
     615             : StaticAssertDecl(RT_FANOUT_48 <= RT_FANOUT_48_MAX, "more slots than isset bits");
     616             : 
     617             : /*
     618             :  * Node size classes
     619             :  *
     620             :  * Nodes of different kinds necessarily belong to different size classes.
     621             :  * One innovation in our implementation compared to the ART paper is
     622             :  * decoupling the notion of size class from kind.
     623             :  *
     624             :  * The size classes within a given node kind have the same underlying
     625             :  * type, but a variable number of children/values. This is possible
     626             :  * because each type (except node256) contains metadata that work the
     627             :  * same way regardless of how many child slots there are. The nodes
     628             :  * can introspect their allocated capacity at runtime.
     629             :  */
     630             : typedef enum RT_SIZE_CLASS
     631             : {
     632             :     RT_CLASS_4 = 0,
     633             :     RT_CLASS_16_LO,
     634             :     RT_CLASS_16_HI,
     635             :     RT_CLASS_48,
     636             :     RT_CLASS_256
     637             : }           RT_SIZE_CLASS;
     638             : 
     639             : /* Information for each size class */
     640             : typedef struct RT_SIZE_CLASS_ELEM
     641             : {
     642             :     const char *name;
     643             :     int         fanout;
     644             :     size_t      allocsize;
     645             : }           RT_SIZE_CLASS_ELEM;
     646             : 
     647             : 
     648             : static const RT_SIZE_CLASS_ELEM RT_SIZE_CLASS_INFO[] = {
     649             :     [RT_CLASS_4] = {
     650             :         .name = RT_STR(RT_PREFIX) "_radix_tree node4",
     651             :         .fanout = RT_FANOUT_4,
     652             :         .allocsize = sizeof(RT_NODE_4) + RT_FANOUT_4 * sizeof(RT_PTR_ALLOC),
     653             :     },
     654             :     [RT_CLASS_16_LO] = {
     655             :         .name = RT_STR(RT_PREFIX) "_radix_tree node16_lo",
     656             :         .fanout = RT_FANOUT_16_LO,
     657             :         .allocsize = sizeof(RT_NODE_16) + RT_FANOUT_16_LO * sizeof(RT_PTR_ALLOC),
     658             :     },
     659             :     [RT_CLASS_16_HI] = {
     660             :         .name = RT_STR(RT_PREFIX) "_radix_tree node16_hi",
     661             :         .fanout = RT_FANOUT_16_HI,
     662             :         .allocsize = sizeof(RT_NODE_16) + RT_FANOUT_16_HI * sizeof(RT_PTR_ALLOC),
     663             :     },
     664             :     [RT_CLASS_48] = {
     665             :         .name = RT_STR(RT_PREFIX) "_radix_tree node48",
     666             :         .fanout = RT_FANOUT_48,
     667             :         .allocsize = sizeof(RT_NODE_48) + RT_FANOUT_48 * sizeof(RT_PTR_ALLOC),
     668             :     },
     669             :     [RT_CLASS_256] = {
     670             :         .name = RT_STR(RT_PREFIX) "_radix_tree node256",
     671             :         .fanout = RT_FANOUT_256,
     672             :         .allocsize = sizeof(RT_NODE_256),
     673             :     },
     674             : };
     675             : 
     676             : #define RT_NUM_SIZE_CLASSES lengthof(RT_SIZE_CLASS_INFO)
     677             : 
     678             : #ifdef RT_SHMEM
     679             : /* A magic value used to identify our radix tree */
     680             : #define RT_RADIX_TREE_MAGIC 0x54A48167
     681             : #endif
     682             : 
     683             : /* Contains the actual tree, plus ancillary info */
     684             : typedef struct RT_RADIX_TREE_CONTROL
     685             : {
     686             : #ifdef RT_SHMEM
     687             :     RT_HANDLE   handle;
     688             :     uint32      magic;
     689             :     LWLock      lock;
     690             : #endif
     691             : 
     692             :     RT_PTR_ALLOC root;
     693             :     uint64      max_val;
     694             :     int64       num_keys;
     695             :     int         start_shift;
     696             : 
     697             :     /* statistics */
     698             : #ifdef RT_DEBUG
     699             :     int64       num_nodes[RT_NUM_SIZE_CLASSES];
     700             :     int64       num_leaves;
     701             : #endif
     702             : }           RT_RADIX_TREE_CONTROL;
     703             : 
     704             : /* Entry point for allocating and accessing the tree */
     705             : struct RT_RADIX_TREE
     706             : {
     707             :     MemoryContext context;
     708             : 
     709             :     /* pointing to either local memory or DSA */
     710             :     RT_RADIX_TREE_CONTROL *ctl;
     711             : 
     712             : #ifdef RT_SHMEM
     713             :     dsa_area   *dsa;
     714             : #else
     715             :     MemoryContextData *node_slabs[RT_NUM_SIZE_CLASSES];
     716             : 
     717             :     /* leaf_context is used only for single-value leaves */
     718             :     MemoryContextData *leaf_context;
     719             : #endif
     720             :     MemoryContextData *iter_context;
     721             : };
     722             : 
     723             : /*
     724             :  * Iteration support.
     725             :  *
     726             :  * Iterating over the radix tree produces each key/value pair in ascending
     727             :  * order of the key.
     728             :  */
     729             : 
     730             : /* state for iterating over a single node */
     731             : typedef struct RT_NODE_ITER
     732             : {
     733             :     RT_CHILD_PTR node;
     734             : 
     735             :     /*
     736             :      * The next index of the chunk array in RT_NODE_KIND_4 and RT_NODE_KIND_16
     737             :      * nodes, or the next chunk in RT_NODE_KIND_48 and RT_NODE_KIND_256 nodes.
     738             :      * 0 for the initial value.
     739             :      */
     740             :     int         idx;
     741             : }           RT_NODE_ITER;
     742             : 
     743             : /* state for iterating over the whole radix tree */
     744             : struct RT_ITER
     745             : {
     746             :     RT_RADIX_TREE *tree;
     747             : 
     748             :     /*
     749             :      * A stack to track iteration for each level. Level 0 is the lowest (or
     750             :      * leaf) level
     751             :      */
     752             :     RT_NODE_ITER node_iters[RT_MAX_LEVEL];
     753             :     int         top_level;
     754             :     int         cur_level;
     755             : 
     756             :     /* The key constructed during iteration */
     757             :     uint64      key;
     758             : };
     759             : 
     760             : 
     761             : /* verification (available only in assert-enabled builds) */
     762             : static void RT_VERIFY_NODE(RT_NODE * node);
     763             : 
     764             : static inline void
     765    35052668 : RT_PTR_SET_LOCAL(RT_RADIX_TREE * tree, RT_CHILD_PTR * node)
     766             : {
     767             : #ifdef RT_SHMEM
     768     2155904 :     node->local = dsa_get_address(tree->dsa, node->alloc);
     769             : #endif
     770    35052668 : }
     771             : 
     772             : /* Convenience functions for node48 and node256 */
     773             : 
     774             : /* Return true if there is an entry for "chunk" */
     775             : static inline bool
     776     1056444 : RT_NODE_48_IS_CHUNK_USED(RT_NODE_48 * node, uint8 chunk)
     777             : {
     778     1056444 :     return node->slot_idxs[chunk] != RT_INVALID_SLOT_IDX;
     779             : }
     780             : 
     781             : static inline RT_PTR_ALLOC *
     782     1052434 : RT_NODE_48_GET_CHILD(RT_NODE_48 * node, uint8 chunk)
     783             : {
     784     1052434 :     return &node->children[node->slot_idxs[chunk]];
     785             : }
     786             : 
     787             : /* Return true if there is an entry for "chunk" */
     788             : static inline bool
     789     7926274 : RT_NODE_256_IS_CHUNK_USED(RT_NODE_256 * node, uint8 chunk)
     790             : {
     791     7926274 :     int         idx = RT_BM_IDX(chunk);
     792     7926274 :     int         bitnum = RT_BM_BIT(chunk);
     793             : 
     794     7926274 :     return (node->isset[idx] & ((bitmapword) 1 << bitnum)) != 0;
     795             : }
     796             : 
     797             : static inline RT_PTR_ALLOC *
     798     7783294 : RT_NODE_256_GET_CHILD(RT_NODE_256 * node, uint8 chunk)
     799             : {
     800             :     Assert(RT_NODE_256_IS_CHUNK_USED(node, chunk));
     801     7783294 :     return &node->children[chunk];
     802             : }
     803             : 
     804             : /*
     805             :  * Return the smallest shift that will allowing storing the given key.
     806             :  */
     807             : static inline int
     808       20454 : RT_KEY_GET_SHIFT(uint64 key)
     809             : {
     810       20454 :     if (key == 0)
     811           0 :         return 0;
     812             :     else
     813       20454 :         return (pg_leftmost_one_pos64(key) / RT_SPAN) * RT_SPAN;
     814             : }
     815             : 
     816             : /*
     817             :  * Return the max value that can be stored in the tree with the given shift.
     818             :  */
     819             : static uint64
     820       20386 : RT_SHIFT_GET_MAX_VAL(int shift)
     821             : {
     822       20386 :     if (shift == RT_MAX_SHIFT)
     823          20 :         return UINT64_MAX;
     824             :     else
     825       20366 :         return (UINT64CONST(1) << (shift + RT_SPAN)) - 1;
     826             : }
     827             : 
     828             : /*
     829             :  * Allocate a new node with the given node kind and size class.
     830             :  */
     831             : static inline RT_CHILD_PTR
     832       73392 : RT_ALLOC_NODE(RT_RADIX_TREE * tree, const uint8 kind, const RT_SIZE_CLASS size_class)
     833             : {
     834             :     RT_CHILD_PTR allocnode;
     835             :     RT_NODE    *node;
     836             :     size_t      allocsize;
     837             : 
     838       73392 :     allocsize = RT_SIZE_CLASS_INFO[size_class].allocsize;
     839             : 
     840             : #ifdef RT_SHMEM
     841         102 :     allocnode.alloc = dsa_allocate(tree->dsa, allocsize);
     842             : #else
     843       73290 :     allocnode.alloc = (RT_PTR_ALLOC) MemoryContextAlloc(tree->node_slabs[size_class],
     844             :                                                         allocsize);
     845             : #endif
     846             : 
     847       73392 :     RT_PTR_SET_LOCAL(tree, &allocnode);
     848       73392 :     node = allocnode.local;
     849             : 
     850             :     /* initialize contents */
     851             : 
     852       73392 :     switch (kind)
     853             :     {
     854       55944 :         case RT_NODE_KIND_4:
     855       55944 :             memset(node, 0, offsetof(RT_NODE_4, children));
     856       55944 :             break;
     857       13036 :         case RT_NODE_KIND_16:
     858       13036 :             memset(node, 0, offsetof(RT_NODE_16, children));
     859       13036 :             break;
     860        4290 :         case RT_NODE_KIND_48:
     861             :             {
     862        4290 :                 RT_NODE_48 *n48 = (RT_NODE_48 *) node;
     863             : 
     864        4290 :                 memset(n48, 0, offsetof(RT_NODE_48, slot_idxs));
     865        4290 :                 memset(n48->slot_idxs, RT_INVALID_SLOT_IDX, sizeof(n48->slot_idxs));
     866        4290 :                 break;
     867             :             }
     868         122 :         case RT_NODE_KIND_256:
     869         122 :             memset(node, 0, offsetof(RT_NODE_256, children));
     870         122 :             break;
     871           0 :         default:
     872           0 :             pg_unreachable();
     873             :     }
     874             : 
     875       73392 :     node->kind = kind;
     876             : 
     877             :     /*
     878             :      * For node256, this will actually overflow to zero, but that's okay
     879             :      * because that node doesn't need to introspect this value.
     880             :      */
     881       73392 :     node->fanout = RT_SIZE_CLASS_INFO[size_class].fanout;
     882             : 
     883             : #ifdef RT_DEBUG
     884             :     /* update the statistics */
     885       52160 :     tree->ctl->num_nodes[size_class]++;
     886             : #endif
     887             : 
     888       73392 :     return allocnode;
     889             : }
     890             : 
     891             : /*
     892             :  * Allocate a new leaf.
     893             :  */
     894             : static RT_CHILD_PTR
     895       20284 : RT_ALLOC_LEAF(RT_RADIX_TREE * tree, size_t allocsize)
     896             : {
     897             :     RT_CHILD_PTR leaf;
     898             : 
     899             : #ifdef RT_SHMEM
     900        1232 :     leaf.alloc = dsa_allocate(tree->dsa, allocsize);
     901        1232 :     RT_PTR_SET_LOCAL(tree, &leaf);
     902             : #else
     903       19052 :     leaf.alloc = (RT_PTR_ALLOC) MemoryContextAlloc(tree->leaf_context, allocsize);
     904             : #endif
     905             : 
     906             : #ifdef RT_DEBUG
     907           0 :     tree->ctl->num_leaves++;
     908             : #endif
     909             : 
     910       20284 :     return leaf;
     911             : }
     912             : 
     913             : /*
     914             :  * Copy relevant members of the node header.
     915             :  * This is a separate function in case other fields are added.
     916             :  */
     917             : static inline void
     918       21610 : RT_COPY_COMMON(RT_CHILD_PTR newnode, RT_CHILD_PTR oldnode)
     919             : {
     920       21610 :     (newnode.local)->count = (oldnode.local)->count;
     921       21610 : }
     922             : 
     923             : /* Free the given node */
     924             : static void
     925       53050 : RT_FREE_NODE(RT_RADIX_TREE * tree, RT_CHILD_PTR node)
     926             : {
     927             : #ifdef RT_DEBUG
     928             :     int         i;
     929             : 
     930             :     /* update the statistics */
     931             : 
     932       81074 :     for (i = 0; i < RT_NUM_SIZE_CLASSES; i++)
     933             :     {
     934       81036 :         if ((node.local)->fanout == RT_SIZE_CLASS_INFO[i].fanout)
     935       52058 :             break;
     936             :     }
     937             : 
     938             :     /*
     939             :      * The fanout of node256 will appear to be zero within the node header
     940             :      * because of overflow, so we need an extra check here.
     941             :      */
     942       52096 :     if (i == RT_NUM_SIZE_CLASSES)
     943          38 :         i = RT_CLASS_256;
     944             : 
     945       52096 :     tree->ctl->num_nodes[i]--;
     946             :     Assert(tree->ctl->num_nodes[i] >= 0);
     947             : #endif
     948             : 
     949             : #ifdef RT_SHMEM
     950          56 :     dsa_free(tree->dsa, node.alloc);
     951             : #else
     952       52994 :     pfree(node.alloc);
     953             : #endif
     954       53050 : }
     955             : 
     956             : static inline void
     957           6 : RT_FREE_LEAF(RT_RADIX_TREE * tree, RT_PTR_ALLOC leaf)
     958             : {
     959             :     Assert(leaf != tree->ctl->root);
     960             : 
     961             : #ifdef RT_DEBUG
     962             :     /* update the statistics */
     963           0 :     tree->ctl->num_leaves--;
     964             :     Assert(tree->ctl->num_leaves >= 0);
     965             : #endif
     966             : 
     967             : #ifdef RT_SHMEM
     968           0 :     dsa_free(tree->dsa, leaf);
     969             : #else
     970           6 :     pfree(leaf);
     971             : #endif
     972           6 : }
     973             : 
     974             : /***************** SEARCH *****************/
     975             : 
     976             : /*
     977             :  * Return the address of the child corresponding to "chunk",
     978             :  * or NULL if there is no such element.
     979             :  */
     980             : static inline RT_PTR_ALLOC *
     981     5910326 : RT_NODE_16_SEARCH_EQ(RT_NODE_16 * node, uint8 chunk)
     982             : {
     983     5910326 :     int         count = node->base.count;
     984             : #ifndef USE_NO_SIMD
     985             :     Vector8     spread_chunk;
     986             :     Vector8     haystack1;
     987             :     Vector8     haystack2;
     988             :     Vector8     cmp1;
     989             :     Vector8     cmp2;
     990             :     uint32      bitfield;
     991     5910326 :     RT_PTR_ALLOC *slot_simd = NULL;
     992             : #endif
     993             : 
     994             : #if defined(USE_NO_SIMD) || defined(USE_ASSERT_CHECKING)
     995             :     RT_PTR_ALLOC *slot = NULL;
     996             : 
     997             :     for (int i = 0; i < count; i++)
     998             :     {
     999             :         if (node->chunks[i] == chunk)
    1000             :         {
    1001             :             slot = &node->children[i];
    1002             :             break;
    1003             :         }
    1004             :     }
    1005             : #endif
    1006             : 
    1007             : #ifndef USE_NO_SIMD
    1008             :     /* replicate the search key */
    1009     5910326 :     spread_chunk = vector8_broadcast(chunk);
    1010             : 
    1011             :     /* compare to all 32 keys stored in the node */
    1012     5910326 :     vector8_load(&haystack1, &node->chunks[0]);
    1013     5910326 :     vector8_load(&haystack2, &node->chunks[sizeof(Vector8)]);
    1014     5910326 :     cmp1 = vector8_eq(spread_chunk, haystack1);
    1015     5910326 :     cmp2 = vector8_eq(spread_chunk, haystack2);
    1016             : 
    1017             :     /* convert comparison to a bitfield */
    1018     5910326 :     bitfield = vector8_highbit_mask(cmp1) | (vector8_highbit_mask(cmp2) << sizeof(Vector8));
    1019             : 
    1020             :     /* mask off invalid entries */
    1021     5910326 :     bitfield &= ((UINT64CONST(1) << count) - 1);
    1022             : 
    1023             :     /* convert bitfield to index by counting trailing zeros */
    1024     5910326 :     if (bitfield)
    1025     5440018 :         slot_simd = &node->children[pg_rightmost_one_pos32(bitfield)];
    1026             : 
    1027             :     Assert(slot_simd == slot);
    1028     5910326 :     return slot_simd;
    1029             : #else
    1030             :     return slot;
    1031             : #endif
    1032             : }
    1033             : 
    1034             : /*
    1035             :  * Search for the child pointer corresponding to "key" in the given node.
    1036             :  *
    1037             :  * Return child if the key is found, otherwise return NULL.
    1038             :  */
    1039             : static inline RT_PTR_ALLOC *
    1040    27015634 : RT_NODE_SEARCH(RT_NODE * node, uint8 chunk)
    1041             : {
    1042             :     /* Make sure we already converted to local pointer */
    1043             :     Assert(node != NULL);
    1044             : 
    1045    27015634 :     switch (node->kind)
    1046             :     {
    1047    11765584 :         case RT_NODE_KIND_4:
    1048             :             {
    1049    11765584 :                 RT_NODE_4  *n4 = (RT_NODE_4 *) node;
    1050             : 
    1051    14478820 :                 for (int i = 0; i < n4->base.count; i++)
    1052             :                 {
    1053    13642010 :                     if (n4->chunks[i] == chunk)
    1054    10928774 :                         return &n4->children[i];
    1055             :                 }
    1056      836810 :                 return NULL;
    1057             :             }
    1058     5910326 :         case RT_NODE_KIND_16:
    1059     5910326 :             return RT_NODE_16_SEARCH_EQ((RT_NODE_16 *) node, chunk);
    1060     1456458 :         case RT_NODE_KIND_48:
    1061             :             {
    1062     1456458 :                 RT_NODE_48 *n48 = (RT_NODE_48 *) node;
    1063     1456458 :                 int         slotpos = n48->slot_idxs[chunk];
    1064             : 
    1065     1456458 :                 if (slotpos == RT_INVALID_SLOT_IDX)
    1066      588740 :                     return NULL;
    1067             : 
    1068      867718 :                 return RT_NODE_48_GET_CHILD(n48, chunk);
    1069             :             }
    1070     7883266 :         case RT_NODE_KIND_256:
    1071             :             {
    1072     7883266 :                 RT_NODE_256 *n256 = (RT_NODE_256 *) node;
    1073             : 
    1074     7883266 :                 if (!RT_NODE_256_IS_CHUNK_USED(n256, chunk))
    1075      142926 :                     return NULL;
    1076             : 
    1077     7740340 :                 return RT_NODE_256_GET_CHILD(n256, chunk);
    1078             :             }
    1079           0 :         default:
    1080           0 :             pg_unreachable();
    1081             :     }
    1082             : }
    1083             : 
    1084             : /*
    1085             :  * Search the given key in the radix tree. Return the pointer to the value if found,
    1086             :  * otherwise return NULL.
    1087             :  *
    1088             :  * Since the function returns a pointer (to support variable-length values),
    1089             :  * the caller is responsible for locking until it's finished with the value.
    1090             :  */
    1091             : RT_SCOPE    RT_VALUE_TYPE *
    1092    10186408 : RT_FIND(RT_RADIX_TREE * tree, uint64 key)
    1093             : {
    1094             :     RT_CHILD_PTR node;
    1095    10186408 :     RT_PTR_ALLOC *slot = NULL;
    1096             :     int         shift;
    1097             : 
    1098             : #ifdef RT_SHMEM
    1099             :     Assert(tree->ctl->magic == RT_RADIX_TREE_MAGIC);
    1100             : #endif
    1101             : 
    1102    10186408 :     if (key > tree->ctl->max_val)
    1103        2866 :         return NULL;
    1104             : 
    1105             :     Assert(RT_PTR_ALLOC_IS_VALID(tree->ctl->root));
    1106    10183542 :     node.alloc = tree->ctl->root;
    1107    10183542 :     shift = tree->ctl->start_shift;
    1108             : 
    1109             :     /* Descend the tree */
    1110    33711918 :     while (shift >= 0)
    1111             :     {
    1112    25335088 :         RT_PTR_SET_LOCAL(tree, &node);
    1113    25335088 :         slot = RT_NODE_SEARCH(node.local, RT_GET_KEY_CHUNK(key, shift));
    1114    25335088 :         if (slot == NULL)
    1115     1806712 :             return NULL;
    1116             : 
    1117    23528376 :         node.alloc = *slot;
    1118    23528376 :         shift -= RT_SPAN;
    1119             :     }
    1120             : 
    1121     8376830 :     if (RT_CHILDPTR_IS_VALUE(*slot))
    1122      455532 :         return (RT_VALUE_TYPE *) slot;
    1123             :     else
    1124             :     {
    1125     7921298 :         RT_PTR_SET_LOCAL(tree, &node);
    1126     7921298 :         return (RT_VALUE_TYPE *) node.local;
    1127             :     }
    1128             : }
    1129             : 
    1130             : /***************** INSERTION *****************/
    1131             : 
    1132             : #define RT_NODE_MUST_GROW(node) \
    1133             :     ((node)->count == (node)->fanout)
    1134             : 
    1135             : /*
    1136             :  * Return index of the chunk and slot arrays for inserting into the node,
    1137             :  * such that the arrays remain ordered.
    1138             :  */
    1139             : static inline int
    1140       19750 : RT_NODE_4_GET_INSERTPOS(RT_NODE_4 * node, uint8 chunk, int count)
    1141             : {
    1142             :     int         idx;
    1143             : 
    1144       45538 :     for (idx = 0; idx < count; idx++)
    1145             :     {
    1146       36980 :         if (node->chunks[idx] >= chunk)
    1147       11192 :             break;
    1148             :     }
    1149             : 
    1150       19750 :     return idx;
    1151             : }
    1152             : 
    1153             : /*
    1154             :  * Return index of the chunk and slot arrays for inserting into the node,
    1155             :  * such that the arrays remain ordered.
    1156             :  */
    1157             : static inline int
    1158      119230 : RT_NODE_16_GET_INSERTPOS(RT_NODE_16 * node, uint8 chunk)
    1159             : {
    1160      119230 :     int         count = node->base.count;
    1161             : #if defined(USE_NO_SIMD) || defined(USE_ASSERT_CHECKING)
    1162             :     int         index;
    1163             : #endif
    1164             : 
    1165             : #ifndef USE_NO_SIMD
    1166             :     Vector8     spread_chunk;
    1167             :     Vector8     haystack1;
    1168             :     Vector8     haystack2;
    1169             :     Vector8     cmp1;
    1170             :     Vector8     cmp2;
    1171             :     Vector8     min1;
    1172             :     Vector8     min2;
    1173             :     uint32      bitfield;
    1174             :     int         index_simd;
    1175             : #endif
    1176             : 
    1177             :     /*
    1178             :      * First compare the last element. There are two reasons to branch here:
    1179             :      *
    1180             :      * 1) A realistic pattern is inserting ordered keys. In that case,
    1181             :      * non-SIMD platforms must do a linear search to the last chunk to find
    1182             :      * the insert position. This will get slower as the node fills up.
    1183             :      *
    1184             :      * 2) On SIMD platforms, we must branch anyway to make sure we don't bit
    1185             :      * scan an empty bitfield. Doing the branch here eliminates some work that
    1186             :      * we might otherwise throw away.
    1187             :      */
    1188             :     Assert(count > 0);
    1189      119230 :     if (node->chunks[count - 1] < chunk)
    1190       14698 :         return count;
    1191             : 
    1192             : #if defined(USE_NO_SIMD) || defined(USE_ASSERT_CHECKING)
    1193             : 
    1194             :     for (index = 0; index < count; index++)
    1195             :     {
    1196             :         if (node->chunks[index] > chunk)
    1197             :             break;
    1198             :     }
    1199             : #endif
    1200             : 
    1201             : #ifndef USE_NO_SIMD
    1202             : 
    1203             :     /*
    1204             :      * This is a bit more complicated than RT_NODE_16_SEARCH_EQ(), because no
    1205             :      * unsigned uint8 comparison instruction exists, at least for SSE2. So we
    1206             :      * need to play some trickery using vector8_min() to effectively get >=.
    1207             :      * There'll never be any equal elements in current uses, but that's what
    1208             :      * we get here...
    1209             :      */
    1210      104532 :     spread_chunk = vector8_broadcast(chunk);
    1211      104532 :     vector8_load(&haystack1, &node->chunks[0]);
    1212      104532 :     vector8_load(&haystack2, &node->chunks[sizeof(Vector8)]);
    1213      104532 :     min1 = vector8_min(spread_chunk, haystack1);
    1214      104532 :     min2 = vector8_min(spread_chunk, haystack2);
    1215      104532 :     cmp1 = vector8_eq(spread_chunk, min1);
    1216      104532 :     cmp2 = vector8_eq(spread_chunk, min2);
    1217      104532 :     bitfield = vector8_highbit_mask(cmp1) | (vector8_highbit_mask(cmp2) << sizeof(Vector8));
    1218             : 
    1219             :     Assert((bitfield & ((UINT64CONST(1) << count) - 1)) != 0);
    1220      104532 :     index_simd = pg_rightmost_one_pos32(bitfield);
    1221             : 
    1222             :     Assert(index_simd == index);
    1223      104532 :     return index_simd;
    1224             : #else
    1225             :     return index;
    1226             : #endif
    1227             : }
    1228             : 
    1229             : /* Shift the elements right at "insertpos" by one */
    1230             : static inline void
    1231      129998 : RT_SHIFT_ARRAYS_FOR_INSERT(uint8 *chunks, RT_PTR_ALLOC * children, int count, int insertpos)
    1232             : {
    1233             :     /*
    1234             :      * This is basically a memmove, but written in a simple loop for speed on
    1235             :      * small inputs.
    1236             :      */
    1237     1122172 :     for (int i = count - 1; i >= insertpos; i--)
    1238             :     {
    1239             :         /* workaround for https://gcc.gnu.org/bugzilla/show_bug.cgi?id=101481 */
    1240             : #ifdef __GNUC__
    1241      992174 :         __asm__("");
    1242             : #endif
    1243      992174 :         chunks[i + 1] = chunks[i];
    1244      992174 :         children[i + 1] = children[i];
    1245             :     }
    1246      129998 : }
    1247             : 
    1248             : /*
    1249             :  * Copy both chunk and slot arrays into the right
    1250             :  * place. The caller is responsible for inserting the new element.
    1251             :  */
    1252             : static inline void
    1253        8982 : RT_COPY_ARRAYS_FOR_INSERT(uint8 *dst_chunks, RT_PTR_ALLOC * dst_children,
    1254             :                           uint8 *src_chunks, RT_PTR_ALLOC * src_children,
    1255             :                           int count, int insertpos)
    1256             : {
    1257       97646 :     for (int i = 0; i < count; i++)
    1258             :     {
    1259       88664 :         int         sourceidx = i;
    1260             : 
    1261             :         /* use a branch-free computation to skip the index of the new element */
    1262       88664 :         int         destidx = i + (i >= insertpos);
    1263             : 
    1264       88664 :         dst_chunks[destidx] = src_chunks[sourceidx];
    1265       88664 :         dst_children[destidx] = src_children[sourceidx];
    1266             :     }
    1267        8982 : }
    1268             : 
    1269             : static inline RT_PTR_ALLOC *
    1270       18670 : RT_ADD_CHILD_256(RT_RADIX_TREE * tree, RT_CHILD_PTR node, uint8 chunk)
    1271             : {
    1272       18670 :     RT_NODE_256 *n256 = (RT_NODE_256 *) node.local;
    1273       18670 :     int         idx = RT_BM_IDX(chunk);
    1274       18670 :     int         bitnum = RT_BM_BIT(chunk);
    1275             : 
    1276             :     /* Mark the slot used for "chunk" */
    1277       18670 :     n256->isset[idx] |= ((bitmapword) 1 << bitnum);
    1278             : 
    1279       18670 :     n256->base.count++;
    1280       18670 :     RT_VERIFY_NODE((RT_NODE *) n256);
    1281             : 
    1282       18670 :     return RT_NODE_256_GET_CHILD(n256, chunk);
    1283             : }
    1284             : 
    1285             : static pg_noinline RT_PTR_ALLOC *
    1286         122 : RT_GROW_NODE_48(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, RT_CHILD_PTR node,
    1287             :                 uint8 chunk)
    1288             : {
    1289         122 :     RT_NODE_48 *n48 = (RT_NODE_48 *) node.local;
    1290             :     RT_CHILD_PTR newnode;
    1291             :     RT_NODE_256 *new256;
    1292         122 :     int         i = 0;
    1293             : 
    1294             :     /* initialize new node */
    1295         122 :     newnode = RT_ALLOC_NODE(tree, RT_NODE_KIND_256, RT_CLASS_256);
    1296         122 :     new256 = (RT_NODE_256 *) newnode.local;
    1297             : 
    1298             :     /* copy over the entries */
    1299         122 :     RT_COPY_COMMON(newnode, node);
    1300         610 :     for (int word_num = 0; word_num < RT_BM_IDX(RT_NODE_MAX_SLOTS); word_num++)
    1301             :     {
    1302         488 :         bitmapword  bitmap = 0;
    1303             : 
    1304             :         /*
    1305             :          * Bit manipulation is a surprisingly large portion of the overhead in
    1306             :          * the naive implementation. Doing stores word-at-a-time removes a lot
    1307             :          * of that overhead.
    1308             :          */
    1309       31720 :         for (int bit = 0; bit < BITS_PER_BITMAPWORD; bit++)
    1310             :         {
    1311       31232 :             uint8       offset = n48->slot_idxs[i];
    1312             : 
    1313       31232 :             if (offset != RT_INVALID_SLOT_IDX)
    1314             :             {
    1315        7792 :                 bitmap |= ((bitmapword) 1 << bit);
    1316        7792 :                 new256->children[i] = n48->children[offset];
    1317             :             }
    1318             : 
    1319       31232 :             i++;
    1320             :         }
    1321             : 
    1322         488 :         new256->isset[word_num] = bitmap;
    1323             :     }
    1324             : 
    1325             :     /* free old node and update reference in parent */
    1326         122 :     *parent_slot = newnode.alloc;
    1327         122 :     RT_FREE_NODE(tree, node);
    1328             : 
    1329         122 :     return RT_ADD_CHILD_256(tree, newnode, chunk);
    1330             : }
    1331             : 
    1332             : static inline RT_PTR_ALLOC *
    1333       52642 : RT_ADD_CHILD_48(RT_RADIX_TREE * tree, RT_CHILD_PTR node, uint8 chunk)
    1334             : {
    1335       52642 :     RT_NODE_48 *n48 = (RT_NODE_48 *) node.local;
    1336             :     int         insertpos;
    1337       52642 :     int         idx = 0;
    1338             :     bitmapword  w,
    1339             :                 inverse;
    1340             : 
    1341             :     /* get the first word with at least one bit not set */
    1342       52642 :     for (int i = 0; i < RT_BM_IDX(RT_FANOUT_48_MAX); i++)
    1343             :     {
    1344       52642 :         w = n48->isset[i];
    1345       52642 :         if (w < ~((bitmapword) 0))
    1346             :         {
    1347       52642 :             idx = i;
    1348       52642 :             break;
    1349             :         }
    1350             :     }
    1351             : 
    1352             :     /* To get the first unset bit in w, get the first set bit in ~w */
    1353       52642 :     inverse = ~w;
    1354       52642 :     insertpos = idx * BITS_PER_BITMAPWORD;
    1355       52642 :     insertpos += bmw_rightmost_one_pos(inverse);
    1356             :     Assert(insertpos < n48->base.fanout);
    1357             : 
    1358             :     /* mark the slot used by setting the rightmost zero bit */
    1359       52642 :     n48->isset[idx] |= w + 1;
    1360             : 
    1361             :     /* insert new chunk into place */
    1362       52642 :     n48->slot_idxs[chunk] = insertpos;
    1363             : 
    1364       52642 :     n48->base.count++;
    1365       52642 :     RT_VERIFY_NODE((RT_NODE *) n48);
    1366             : 
    1367       52642 :     return &n48->children[insertpos];
    1368             : }
    1369             : 
    1370             : static pg_noinline RT_PTR_ALLOC *
    1371        8648 : RT_GROW_NODE_16(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, RT_CHILD_PTR node,
    1372             :                 uint8 chunk)
    1373             : {
    1374        8648 :     RT_NODE_16 *n16 = (RT_NODE_16 *) node.local;
    1375             :     int         insertpos;
    1376             : 
    1377        8648 :     if (n16->base.fanout < RT_FANOUT_16_HI)
    1378             :     {
    1379             :         RT_CHILD_PTR newnode;
    1380             :         RT_NODE_16 *new16;
    1381             : 
    1382             :         Assert(n16->base.fanout == RT_FANOUT_16_LO);
    1383             : 
    1384             :         /* initialize new node */
    1385        4396 :         newnode = RT_ALLOC_NODE(tree, RT_NODE_KIND_16, RT_CLASS_16_HI);
    1386        4396 :         new16 = (RT_NODE_16 *) newnode.local;
    1387             : 
    1388             :         /* copy over existing entries */
    1389        4396 :         RT_COPY_COMMON(newnode, node);
    1390             :         Assert(n16->base.count == RT_FANOUT_16_LO);
    1391        4396 :         insertpos = RT_NODE_16_GET_INSERTPOS(n16, chunk);
    1392        4396 :         RT_COPY_ARRAYS_FOR_INSERT(new16->chunks, new16->children,
    1393        4396 :                                   n16->chunks, n16->children,
    1394             :                                   RT_FANOUT_16_LO, insertpos);
    1395             : 
    1396             :         /* insert new chunk into place */
    1397        4396 :         new16->chunks[insertpos] = chunk;
    1398             : 
    1399        4396 :         new16->base.count++;
    1400        4396 :         RT_VERIFY_NODE((RT_NODE *) new16);
    1401             : 
    1402             :         /* free old node and update references */
    1403        4396 :         RT_FREE_NODE(tree, node);
    1404        4396 :         *parent_slot = newnode.alloc;
    1405             : 
    1406        4396 :         return &new16->children[insertpos];
    1407             :     }
    1408             :     else
    1409             :     {
    1410             :         RT_CHILD_PTR newnode;
    1411             :         RT_NODE_48 *new48;
    1412             :         int         idx,
    1413             :                     bit;
    1414             : 
    1415             :         Assert(n16->base.fanout == RT_FANOUT_16_HI);
    1416             : 
    1417             :         /* initialize new node */
    1418        4252 :         newnode = RT_ALLOC_NODE(tree, RT_NODE_KIND_48, RT_CLASS_48);
    1419        4252 :         new48 = (RT_NODE_48 *) newnode.local;
    1420             : 
    1421             :         /* copy over the entries */
    1422        4252 :         RT_COPY_COMMON(newnode, node);
    1423      140316 :         for (int i = 0; i < RT_FANOUT_16_HI; i++)
    1424      136064 :             new48->slot_idxs[n16->chunks[i]] = i;
    1425        4252 :         memcpy(&new48->children[0], &n16->children[0], RT_FANOUT_16_HI * sizeof(new48->children[0]));
    1426             : 
    1427             :         /*
    1428             :          * Since we just copied a dense array, we can fill "isset" using a
    1429             :          * single store, provided the length of that array is at most the
    1430             :          * number of bits in a bitmapword.
    1431             :          */
    1432             :         Assert(RT_FANOUT_16_HI <= BITS_PER_BITMAPWORD);
    1433        4252 :         new48->isset[0] = (bitmapword) (((uint64) 1 << RT_FANOUT_16_HI) - 1);
    1434             : 
    1435             :         /* put the new child at the end of the copied entries */
    1436        4252 :         insertpos = RT_FANOUT_16_HI;
    1437        4252 :         idx = RT_BM_IDX(insertpos);
    1438        4252 :         bit = RT_BM_BIT(insertpos);
    1439             : 
    1440             :         /* mark the slot used */
    1441        4252 :         new48->isset[idx] |= ((bitmapword) 1 << bit);
    1442             : 
    1443             :         /* insert new chunk into place */
    1444        4252 :         new48->slot_idxs[chunk] = insertpos;
    1445             : 
    1446        4252 :         new48->base.count++;
    1447        4252 :         RT_VERIFY_NODE((RT_NODE *) new48);
    1448             : 
    1449             :         /* free old node and update reference in parent */
    1450        4252 :         *parent_slot = newnode.alloc;
    1451        4252 :         RT_FREE_NODE(tree, node);
    1452             : 
    1453        4252 :         return &new48->children[insertpos];
    1454             :     }
    1455             : }
    1456             : 
    1457             : static inline RT_PTR_ALLOC *
    1458      114834 : RT_ADD_CHILD_16(RT_RADIX_TREE * tree, RT_CHILD_PTR node, uint8 chunk)
    1459             : {
    1460      114834 :     RT_NODE_16 *n16 = (RT_NODE_16 *) node.local;
    1461      114834 :     int         insertpos = RT_NODE_16_GET_INSERTPOS(n16, chunk);
    1462             : 
    1463             :     /* shift chunks and children */
    1464      114834 :     RT_SHIFT_ARRAYS_FOR_INSERT(n16->chunks, n16->children,
    1465      114834 :                                n16->base.count, insertpos);
    1466             : 
    1467             :     /* insert new chunk into place */
    1468      114834 :     n16->chunks[insertpos] = chunk;
    1469             : 
    1470      114834 :     n16->base.count++;
    1471      114834 :     RT_VERIFY_NODE((RT_NODE *) n16);
    1472             : 
    1473      114834 :     return &n16->children[insertpos];
    1474             : }
    1475             : 
    1476             : static pg_noinline RT_PTR_ALLOC *
    1477        4586 : RT_GROW_NODE_4(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, RT_CHILD_PTR node,
    1478             :                uint8 chunk)
    1479             : {
    1480        4586 :     RT_NODE_4  *n4 = (RT_NODE_4 *) (node.local);
    1481             :     RT_CHILD_PTR newnode;
    1482             :     RT_NODE_16 *new16;
    1483             :     int         insertpos;
    1484             : 
    1485             :     /* initialize new node */
    1486        4586 :     newnode = RT_ALLOC_NODE(tree, RT_NODE_KIND_16, RT_CLASS_16_LO);
    1487        4586 :     new16 = (RT_NODE_16 *) newnode.local;
    1488             : 
    1489             :     /* copy over existing entries */
    1490        4586 :     RT_COPY_COMMON(newnode, node);
    1491             :     Assert(n4->base.count == RT_FANOUT_4);
    1492        4586 :     insertpos = RT_NODE_4_GET_INSERTPOS(n4, chunk, RT_FANOUT_4);
    1493        4586 :     RT_COPY_ARRAYS_FOR_INSERT(new16->chunks, new16->children,
    1494        4586 :                               n4->chunks, n4->children,
    1495             :                               RT_FANOUT_4, insertpos);
    1496             : 
    1497             :     /* insert new chunk into place */
    1498        4586 :     new16->chunks[insertpos] = chunk;
    1499             : 
    1500        4586 :     new16->base.count++;
    1501        4586 :     RT_VERIFY_NODE((RT_NODE *) new16);
    1502             : 
    1503             :     /* free old node and update reference in parent */
    1504        4586 :     *parent_slot = newnode.alloc;
    1505        4586 :     RT_FREE_NODE(tree, node);
    1506             : 
    1507        4586 :     return &new16->children[insertpos];
    1508             : }
    1509             : 
    1510             : static inline RT_PTR_ALLOC *
    1511       15164 : RT_ADD_CHILD_4(RT_RADIX_TREE * tree, RT_CHILD_PTR node, uint8 chunk)
    1512             : {
    1513       15164 :     RT_NODE_4  *n4 = (RT_NODE_4 *) (node.local);
    1514       15164 :     int         count = n4->base.count;
    1515       15164 :     int         insertpos = RT_NODE_4_GET_INSERTPOS(n4, chunk, count);
    1516             : 
    1517             :     /* shift chunks and children */
    1518       15164 :     RT_SHIFT_ARRAYS_FOR_INSERT(n4->chunks, n4->children,
    1519             :                                count, insertpos);
    1520             : 
    1521             :     /* insert new chunk into place */
    1522       15164 :     n4->chunks[insertpos] = chunk;
    1523             : 
    1524       15164 :     n4->base.count++;
    1525       15164 :     RT_VERIFY_NODE((RT_NODE *) n4);
    1526             : 
    1527       15164 :     return &n4->children[insertpos];
    1528             : }
    1529             : 
    1530             : /*
    1531             :  * Reserve slot in "node"'s child array. The caller will populate it
    1532             :  * with the actual child pointer.
    1533             :  *
    1534             :  * "parent_slot" is the address of the parent's child pointer to "node".
    1535             :  * If the node we're inserting into needs to grow, we update the parent's
    1536             :  * child pointer with the pointer to the new larger node.
    1537             :  */
    1538             : static inline RT_PTR_ALLOC *
    1539      214544 : RT_NODE_INSERT(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, RT_CHILD_PTR node,
    1540             :                uint8 chunk)
    1541             : {
    1542      214544 :     RT_NODE    *n = node.local;
    1543             : 
    1544      214544 :     switch (n->kind)
    1545             :     {
    1546       19750 :         case RT_NODE_KIND_4:
    1547             :             {
    1548       19750 :                 if (unlikely(RT_NODE_MUST_GROW(n)))
    1549        4586 :                     return RT_GROW_NODE_4(tree, parent_slot, node, chunk);
    1550             : 
    1551       15164 :                 return RT_ADD_CHILD_4(tree, node, chunk);
    1552             :             }
    1553      123482 :         case RT_NODE_KIND_16:
    1554             :             {
    1555      123482 :                 if (unlikely(RT_NODE_MUST_GROW(n)))
    1556        8648 :                     return RT_GROW_NODE_16(tree, parent_slot, node, chunk);
    1557             : 
    1558      114834 :                 return RT_ADD_CHILD_16(tree, node, chunk);
    1559             :             }
    1560       52764 :         case RT_NODE_KIND_48:
    1561             :             {
    1562       52764 :                 if (unlikely(RT_NODE_MUST_GROW(n)))
    1563         122 :                     return RT_GROW_NODE_48(tree, parent_slot, node, chunk);
    1564             : 
    1565       52642 :                 return RT_ADD_CHILD_48(tree, node, chunk);
    1566             :             }
    1567       18548 :         case RT_NODE_KIND_256:
    1568       18548 :             return RT_ADD_CHILD_256(tree, node, chunk);
    1569           0 :         default:
    1570           0 :             pg_unreachable();
    1571             :     }
    1572             : }
    1573             : 
    1574             : /*
    1575             :  * The radix tree doesn't have sufficient height. Put new node(s) on top,
    1576             :  * and move the old node below it.
    1577             :  */
    1578             : static pg_noinline void
    1579          42 : RT_EXTEND_UP(RT_RADIX_TREE * tree, uint64 key)
    1580             : {
    1581          42 :     int         target_shift = RT_KEY_GET_SHIFT(key);
    1582          42 :     int         shift = tree->ctl->start_shift;
    1583             : 
    1584             :     Assert(shift < target_shift);
    1585             : 
    1586             :     /* Grow tree upwards until start shift can accommodate the key */
    1587         144 :     while (shift < target_shift)
    1588             :     {
    1589             :         RT_CHILD_PTR node;
    1590             :         RT_NODE_4  *n4;
    1591             : 
    1592         102 :         node = RT_ALLOC_NODE(tree, RT_NODE_KIND_4, RT_CLASS_4);
    1593         102 :         n4 = (RT_NODE_4 *) node.local;
    1594         102 :         n4->base.count = 1;
    1595         102 :         n4->chunks[0] = 0;
    1596         102 :         n4->children[0] = tree->ctl->root;
    1597             : 
    1598             :         /* Update the root */
    1599         102 :         tree->ctl->root = node.alloc;
    1600             : 
    1601         102 :         shift += RT_SPAN;
    1602             :     }
    1603             : 
    1604          42 :     tree->ctl->max_val = RT_SHIFT_GET_MAX_VAL(target_shift);
    1605          42 :     tree->ctl->start_shift = target_shift;
    1606          42 : }
    1607             : 
    1608             : /*
    1609             :  * Insert a chain of nodes until we reach the lowest level,
    1610             :  * and return the address of a slot to be filled further up
    1611             :  * the call stack.
    1612             :  */
    1613             : static pg_noinline RT_PTR_ALLOC *
    1614        9938 : RT_EXTEND_DOWN(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, uint64 key, int shift)
    1615             : {
    1616             :     RT_CHILD_PTR node,
    1617             :                 child;
    1618             :     RT_NODE_4  *n4;
    1619             : 
    1620             :     /*
    1621             :      * The child pointer of the first node in the chain goes in the
    1622             :      * caller-provided slot.
    1623             :      */
    1624        9938 :     child = RT_ALLOC_NODE(tree, RT_NODE_KIND_4, RT_CLASS_4);
    1625        9938 :     *parent_slot = child.alloc;
    1626             : 
    1627        9938 :     node = child;
    1628        9938 :     shift -= RT_SPAN;
    1629             : 
    1630       31424 :     while (shift > 0)
    1631             :     {
    1632       21486 :         child = RT_ALLOC_NODE(tree, RT_NODE_KIND_4, RT_CLASS_4);
    1633             : 
    1634             :         /* We open-code the insertion ourselves, for speed. */
    1635       21486 :         n4 = (RT_NODE_4 *) node.local;
    1636       21486 :         n4->base.count = 1;
    1637       21486 :         n4->chunks[0] = RT_GET_KEY_CHUNK(key, shift);
    1638       21486 :         n4->children[0] = child.alloc;
    1639             : 
    1640       21486 :         node = child;
    1641       21486 :         shift -= RT_SPAN;
    1642             :     }
    1643             :     Assert(shift == 0);
    1644             : 
    1645             :     /* Reserve slot for the value. */
    1646        9938 :     n4 = (RT_NODE_4 *) node.local;
    1647        9938 :     n4->chunks[0] = RT_GET_KEY_CHUNK(key, 0);
    1648        9938 :     n4->base.count = 1;
    1649             : 
    1650        9938 :     return &n4->children[0];
    1651             : }
    1652             : 
    1653             : /*
    1654             :  * Workhorse for RT_SET
    1655             :  *
    1656             :  * "parent_slot" is the address of the child pointer we just followed,
    1657             :  * in the parent's array of children, needed if inserting into the
    1658             :  * current node causes it to grow.
    1659             :  */
    1660             : static RT_PTR_ALLOC *
    1661      850114 : RT_GET_SLOT_RECURSIVE(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, uint64 key, int shift, bool *found)
    1662             : {
    1663             :     RT_PTR_ALLOC *slot;
    1664             :     RT_CHILD_PTR node;
    1665      850114 :     uint8       chunk = RT_GET_KEY_CHUNK(key, shift);
    1666             : 
    1667      850114 :     node.alloc = *parent_slot;
    1668      850114 :     RT_PTR_SET_LOCAL(tree, &node);
    1669      850114 :     slot = RT_NODE_SEARCH(node.local, chunk);
    1670             : 
    1671      850114 :     if (slot == NULL)
    1672             :     {
    1673      214544 :         *found = false;
    1674             : 
    1675             :         /* reserve slot for the caller to populate */
    1676             : 
    1677      214544 :         slot = RT_NODE_INSERT(tree, parent_slot, node, chunk);
    1678             : 
    1679      214544 :         if (shift == 0)
    1680      204632 :             return slot;
    1681             :         else
    1682        9912 :             return RT_EXTEND_DOWN(tree, slot, key, shift);
    1683             :     }
    1684             :     else
    1685             :     {
    1686      635570 :         if (shift == 0)
    1687             :         {
    1688       21898 :             *found = true;
    1689       21898 :             return slot;
    1690             :         }
    1691             :         else
    1692      613672 :             return RT_GET_SLOT_RECURSIVE(tree, slot, key, shift - RT_SPAN, found);
    1693             :     }
    1694             : }
    1695             : 
    1696             : /*
    1697             :  * Set key to value that value_p points to. If the entry already exists, we
    1698             :  * update its value and return true. Returns false if entry doesn't yet exist.
    1699             :  *
    1700             :  * Taking a lock in exclusive mode is the caller's responsibility.
    1701             :  */
    1702             : RT_SCOPE bool
    1703      236468 : RT_SET(RT_RADIX_TREE * tree, uint64 key, RT_VALUE_TYPE * value_p)
    1704             : {
    1705             :     bool        found;
    1706             :     RT_PTR_ALLOC *slot;
    1707      236468 :     size_t      value_sz = RT_GET_VALUE_SIZE(value_p);
    1708             : 
    1709             : #ifdef RT_SHMEM
    1710             :     Assert(tree->ctl->magic == RT_RADIX_TREE_MAGIC);
    1711             : #endif
    1712             : 
    1713             :     Assert(RT_PTR_ALLOC_IS_VALID(tree->ctl->root));
    1714             : 
    1715             :     /* Extend the tree if necessary */
    1716      236468 :     if (unlikely(key > tree->ctl->max_val))
    1717             :     {
    1718          68 :         if (tree->ctl->num_keys == 0)
    1719             :         {
    1720             :             RT_CHILD_PTR node;
    1721             :             RT_NODE_4  *n4;
    1722          26 :             int         start_shift = RT_KEY_GET_SHIFT(key);
    1723             : 
    1724             :             /*
    1725             :              * With an empty root node, we don't extend the tree upwards,
    1726             :              * since that would result in orphan empty nodes. Instead we open
    1727             :              * code inserting into the root node and extend downward from
    1728             :              * there.
    1729             :              */
    1730          26 :             node.alloc = tree->ctl->root;
    1731          26 :             RT_PTR_SET_LOCAL(tree, &node);
    1732          26 :             n4 = (RT_NODE_4 *) node.local;
    1733          26 :             n4->base.count = 1;
    1734          26 :             n4->chunks[0] = RT_GET_KEY_CHUNK(key, start_shift);
    1735             : 
    1736          26 :             slot = RT_EXTEND_DOWN(tree, &n4->children[0], key, start_shift);
    1737          26 :             found = false;
    1738          26 :             tree->ctl->start_shift = start_shift;
    1739          26 :             tree->ctl->max_val = RT_SHIFT_GET_MAX_VAL(start_shift);
    1740          26 :             goto have_slot;
    1741             :         }
    1742             :         else
    1743          42 :             RT_EXTEND_UP(tree, key);
    1744             :     }
    1745             : 
    1746      236442 :     slot = RT_GET_SLOT_RECURSIVE(tree, &tree->ctl->root,
    1747      236442 :                                  key, tree->ctl->start_shift, &found);
    1748             : 
    1749      236468 : have_slot:
    1750             :     Assert(slot != NULL);
    1751             : 
    1752      236468 :     if (RT_VALUE_IS_EMBEDDABLE(value_p))
    1753             :     {
    1754             :         /* free the existing leaf */
    1755      216184 :         if (found && !RT_CHILDPTR_IS_VALUE(*slot))
    1756           2 :             RT_FREE_LEAF(tree, *slot);
    1757             : 
    1758             :         /* store value directly in child pointer slot */
    1759      216184 :         memcpy(slot, value_p, value_sz);
    1760             : 
    1761             : #ifdef RT_RUNTIME_EMBEDDABLE_VALUE
    1762             :         /* tag child pointer */
    1763             : #ifdef RT_SHMEM
    1764           6 :         *slot |= 1;
    1765             : #else
    1766        3110 :         *((uintptr_t *) slot) |= 1;
    1767             : #endif
    1768             : #endif
    1769             :     }
    1770             :     else
    1771             :     {
    1772             :         RT_CHILD_PTR leaf;
    1773             : 
    1774       20284 :         if (found && !RT_CHILDPTR_IS_VALUE(*slot))
    1775             :         {
    1776             :             Assert(RT_PTR_ALLOC_IS_VALID(*slot));
    1777           4 :             leaf.alloc = *slot;
    1778           4 :             RT_PTR_SET_LOCAL(tree, &leaf);
    1779             : 
    1780           4 :             if (RT_GET_VALUE_SIZE((RT_VALUE_TYPE *) leaf.local) != value_sz)
    1781             :             {
    1782             :                 /*
    1783             :                  * different sizes, so first free the existing leaf before
    1784             :                  * allocating a new one
    1785             :                  */
    1786           4 :                 RT_FREE_LEAF(tree, *slot);
    1787           4 :                 leaf = RT_ALLOC_LEAF(tree, value_sz);
    1788           4 :                 *slot = leaf.alloc;
    1789             :             }
    1790             :         }
    1791             :         else
    1792             :         {
    1793             :             /* allocate new leaf and store it in the child array */
    1794       20280 :             leaf = RT_ALLOC_LEAF(tree, value_sz);
    1795       20280 :             *slot = leaf.alloc;
    1796             :         }
    1797             : 
    1798       20284 :         memcpy(leaf.local, value_p, value_sz);
    1799             :     }
    1800             : 
    1801             :     /* Update the statistics */
    1802      236468 :     if (!found)
    1803      214570 :         tree->ctl->num_keys++;
    1804             : 
    1805      236468 :     return found;
    1806             : }
    1807             : 
    1808             : /***************** SETUP / TEARDOWN *****************/
    1809             : 
    1810             : /*
    1811             :  * Create the radix tree in the given memory context and return it.
    1812             :  *
    1813             :  * All local memory required for a radix tree is allocated in the given
    1814             :  * memory context and its children. Note that RT_FREE() will delete all
    1815             :  * allocated space within the given memory context, so the dsa_area should
    1816             :  * be created in a different context.
    1817             :  */
    1818             : RT_SCOPE    RT_RADIX_TREE *
    1819             : #ifdef RT_SHMEM
    1820          36 : RT_CREATE(MemoryContext ctx, dsa_area *dsa, int tranche_id)
    1821             : #else
    1822       20220 : RT_CREATE(MemoryContext ctx)
    1823             : #endif
    1824             : {
    1825             :     RT_RADIX_TREE *tree;
    1826             :     MemoryContext old_ctx;
    1827             :     RT_CHILD_PTR rootnode;
    1828             : #ifdef RT_SHMEM
    1829             :     dsa_pointer dp;
    1830             : #endif
    1831             : 
    1832       20256 :     old_ctx = MemoryContextSwitchTo(ctx);
    1833             : 
    1834       20256 :     tree = (RT_RADIX_TREE *) palloc0(sizeof(RT_RADIX_TREE));
    1835       20256 :     tree->context = ctx;
    1836             : 
    1837             :     /*
    1838             :      * Separate context for iteration in case the tree context doesn't support
    1839             :      * pfree
    1840             :      */
    1841       20256 :     tree->iter_context = AllocSetContextCreate(ctx,
    1842             :                                                RT_STR(RT_PREFIX) "_radix_tree iter context",
    1843             :                                                ALLOCSET_SMALL_SIZES);
    1844             : 
    1845             : #ifdef RT_SHMEM
    1846          36 :     tree->dsa = dsa;
    1847          36 :     dp = dsa_allocate0(dsa, sizeof(RT_RADIX_TREE_CONTROL));
    1848          36 :     tree->ctl = (RT_RADIX_TREE_CONTROL *) dsa_get_address(dsa, dp);
    1849          36 :     tree->ctl->handle = dp;
    1850          36 :     tree->ctl->magic = RT_RADIX_TREE_MAGIC;
    1851          36 :     LWLockInitialize(&tree->ctl->lock, tranche_id);
    1852             : #else
    1853       20220 :     tree->ctl = (RT_RADIX_TREE_CONTROL *) palloc0(sizeof(RT_RADIX_TREE_CONTROL));
    1854             : 
    1855             :     /* Create a slab context for each size class */
    1856      121320 :     for (int i = 0; i < RT_NUM_SIZE_CLASSES; i++)
    1857             :     {
    1858      101100 :         RT_SIZE_CLASS_ELEM size_class = RT_SIZE_CLASS_INFO[i];
    1859      101100 :         size_t      inner_blocksize = RT_SLAB_BLOCK_SIZE(size_class.allocsize);
    1860             : 
    1861      101100 :         tree->node_slabs[i] = SlabContextCreate(ctx,
    1862             :                                                 size_class.name,
    1863             :                                                 inner_blocksize,
    1864             :                                                 size_class.allocsize);
    1865             :     }
    1866             : 
    1867             :     /* By default we use the passed context for leaves. */
    1868       20220 :     tree->leaf_context = tree->context;
    1869             : 
    1870             : #ifndef RT_VARLEN_VALUE_SIZE
    1871             : 
    1872             :     /*
    1873             :      * For leaves storing fixed-length values, we use a slab context to avoid
    1874             :      * the possibility of space wastage by power-of-2 rounding up.
    1875             :      */
    1876             :     if (sizeof(RT_VALUE_TYPE) > sizeof(RT_PTR_ALLOC))
    1877             :         tree->leaf_context = SlabContextCreate(ctx,
    1878             :                                                RT_STR(RT_PREFIX) "_radix_tree leaf context",
    1879             :                                                RT_SLAB_BLOCK_SIZE(sizeof(RT_VALUE_TYPE)),
    1880             :                                                sizeof(RT_VALUE_TYPE));
    1881             : #endif                          /* !RT_VARLEN_VALUE_SIZE */
    1882             : #endif                          /* RT_SHMEM */
    1883             : 
    1884             :     /* add root node now so that RT_SET can assume it exists */
    1885       20256 :     rootnode = RT_ALLOC_NODE(tree, RT_NODE_KIND_4, RT_CLASS_4);
    1886       20256 :     tree->ctl->root = rootnode.alloc;
    1887       20256 :     tree->ctl->start_shift = 0;
    1888       20256 :     tree->ctl->max_val = RT_SHIFT_GET_MAX_VAL(0);
    1889             : 
    1890       20256 :     MemoryContextSwitchTo(old_ctx);
    1891             : 
    1892       20256 :     return tree;
    1893             : }
    1894             : 
    1895             : #ifdef RT_SHMEM
    1896             : RT_SCOPE    RT_RADIX_TREE *
    1897          36 : RT_ATTACH(dsa_area *dsa, RT_HANDLE handle)
    1898             : {
    1899             :     RT_RADIX_TREE *tree;
    1900             :     dsa_pointer control;
    1901             : 
    1902          36 :     tree = (RT_RADIX_TREE *) palloc0(sizeof(RT_RADIX_TREE));
    1903             : 
    1904             :     /* Find the control object in shared memory */
    1905          36 :     control = handle;
    1906             : 
    1907          36 :     tree->dsa = dsa;
    1908          36 :     tree->ctl = (RT_RADIX_TREE_CONTROL *) dsa_get_address(dsa, control);
    1909             :     Assert(tree->ctl->magic == RT_RADIX_TREE_MAGIC);
    1910             : 
    1911          36 :     return tree;
    1912             : }
    1913             : 
    1914             : RT_SCOPE void
    1915          36 : RT_DETACH(RT_RADIX_TREE * tree)
    1916             : {
    1917             :     Assert(tree->ctl->magic == RT_RADIX_TREE_MAGIC);
    1918          36 :     pfree(tree);
    1919          36 : }
    1920             : 
    1921             : RT_SCOPE    RT_HANDLE
    1922          34 : RT_GET_HANDLE(RT_RADIX_TREE * tree)
    1923             : {
    1924             :     Assert(tree->ctl->magic == RT_RADIX_TREE_MAGIC);
    1925          34 :     return tree->ctl->handle;
    1926             : }
    1927             : 
    1928             : RT_SCOPE void
    1929         206 : RT_LOCK_EXCLUSIVE(RT_RADIX_TREE * tree)
    1930             : {
    1931             :     Assert(tree->ctl->magic == RT_RADIX_TREE_MAGIC);
    1932         206 :     LWLockAcquire(&tree->ctl->lock, LW_EXCLUSIVE);
    1933         206 : }
    1934             : 
    1935             : RT_SCOPE void
    1936      421684 : RT_LOCK_SHARE(RT_RADIX_TREE * tree)
    1937             : {
    1938             :     Assert(tree->ctl->magic == RT_RADIX_TREE_MAGIC);
    1939      421684 :     LWLockAcquire(&tree->ctl->lock, LW_SHARED);
    1940      421684 : }
    1941             : 
    1942             : RT_SCOPE void
    1943      421890 : RT_UNLOCK(RT_RADIX_TREE * tree)
    1944             : {
    1945             :     Assert(tree->ctl->magic == RT_RADIX_TREE_MAGIC);
    1946      421890 :     LWLockRelease(&tree->ctl->lock);
    1947      421890 : }
    1948             : 
    1949             : /*
    1950             :  * Recursively free all nodes allocated in the DSA area.
    1951             :  */
    1952             : static void
    1953          46 : RT_FREE_RECURSE(RT_RADIX_TREE * tree, RT_PTR_ALLOC ptr, int shift)
    1954             : {
    1955             :     RT_CHILD_PTR node;
    1956             : 
    1957          46 :     check_stack_depth();
    1958             : 
    1959          46 :     node.alloc = ptr;
    1960          46 :     RT_PTR_SET_LOCAL(tree, &node);
    1961             : 
    1962          46 :     switch (node.local->kind)
    1963             :     {
    1964          28 :         case RT_NODE_KIND_4:
    1965             :             {
    1966          28 :                 RT_NODE_4  *n4 = (RT_NODE_4 *) node.local;
    1967             : 
    1968          42 :                 for (int i = 0; i < n4->base.count; i++)
    1969             :                 {
    1970          14 :                     RT_PTR_ALLOC child = n4->children[i];
    1971             : 
    1972          14 :                     if (shift > 0)
    1973          10 :                         RT_FREE_RECURSE(tree, child, shift - RT_SPAN);
    1974           4 :                     else if (!RT_CHILDPTR_IS_VALUE(child))
    1975           0 :                         dsa_free(tree->dsa, child);
    1976             :                 }
    1977             : 
    1978          28 :                 break;
    1979             :             }
    1980           4 :         case RT_NODE_KIND_16:
    1981             :             {
    1982           4 :                 RT_NODE_16 *n16 = (RT_NODE_16 *) node.local;
    1983             : 
    1984          74 :                 for (int i = 0; i < n16->base.count; i++)
    1985             :                 {
    1986          70 :                     RT_PTR_ALLOC child = n16->children[i];
    1987             : 
    1988          70 :                     if (shift > 0)
    1989           0 :                         RT_FREE_RECURSE(tree, child, shift - RT_SPAN);
    1990          70 :                     else if (!RT_CHILDPTR_IS_VALUE(child))
    1991          70 :                         dsa_free(tree->dsa, child);
    1992             :                 }
    1993             : 
    1994           4 :                 break;
    1995             :             }
    1996           6 :         case RT_NODE_KIND_48:
    1997             :             {
    1998           6 :                 RT_NODE_48 *n48 = (RT_NODE_48 *) node.local;
    1999             : 
    2000        1542 :                 for (int i = 0; i < RT_NODE_MAX_SLOTS; i++)
    2001             :                 {
    2002             :                     RT_PTR_ALLOC child;
    2003             : 
    2004        1536 :                     if (!RT_NODE_48_IS_CHUNK_USED(n48, i))
    2005        1266 :                         continue;
    2006             : 
    2007         270 :                     child = *RT_NODE_48_GET_CHILD(n48, i);
    2008             : 
    2009         270 :                     if (shift > 0)
    2010           0 :                         RT_FREE_RECURSE(tree, child, shift - RT_SPAN);
    2011         270 :                     else if (!RT_CHILDPTR_IS_VALUE(child))
    2012         270 :                         dsa_free(tree->dsa, child);
    2013             :                 }
    2014             : 
    2015           6 :                 break;
    2016             :             }
    2017           8 :         case RT_NODE_KIND_256:
    2018             :             {
    2019           8 :                 RT_NODE_256 *n256 = (RT_NODE_256 *) node.local;
    2020             : 
    2021        2056 :                 for (int i = 0; i < RT_NODE_MAX_SLOTS; i++)
    2022             :                 {
    2023             :                     RT_PTR_ALLOC child;
    2024             : 
    2025        2048 :                     if (!RT_NODE_256_IS_CHUNK_USED(n256, i))
    2026        1154 :                         continue;
    2027             : 
    2028         894 :                     child = *RT_NODE_256_GET_CHILD(n256, i);
    2029             : 
    2030         894 :                     if (shift > 0)
    2031           0 :                         RT_FREE_RECURSE(tree, child, shift - RT_SPAN);
    2032         894 :                     else if (!RT_CHILDPTR_IS_VALUE(child))
    2033         892 :                         dsa_free(tree->dsa, child);
    2034             :                 }
    2035             : 
    2036           8 :                 break;
    2037             :             }
    2038             :     }
    2039             : 
    2040             :     /* Free the inner node */
    2041          46 :     dsa_free(tree->dsa, ptr);
    2042          46 : }
    2043             : #endif
    2044             : 
    2045             : /*
    2046             :  * Free the radix tree, including all nodes and leaves.
    2047             :  */
    2048             : RT_SCOPE void
    2049        1000 : RT_FREE(RT_RADIX_TREE * tree)
    2050             : {
    2051             : #ifdef RT_SHMEM
    2052             :     Assert(tree->ctl->magic == RT_RADIX_TREE_MAGIC);
    2053             : 
    2054             :     /* Free all memory used for radix tree nodes */
    2055             :     Assert(RT_PTR_ALLOC_IS_VALID(tree->ctl->root));
    2056          36 :     RT_FREE_RECURSE(tree, tree->ctl->root, tree->ctl->start_shift);
    2057             : 
    2058             :     /*
    2059             :      * Vandalize the control block to help catch programming error where other
    2060             :      * backends access the memory formerly occupied by this radix tree.
    2061             :      */
    2062          36 :     tree->ctl->magic = 0;
    2063          36 :     dsa_free(tree->dsa, tree->ctl->handle);
    2064             : #endif
    2065             : 
    2066             :     /*
    2067             :      * Free all space allocated within the tree's context and delete all child
    2068             :      * contexts such as those used for nodes.
    2069             :      */
    2070        1000 :     MemoryContextReset(tree->context);
    2071        1000 : }
    2072             : 
    2073             : /***************** ITERATION *****************/
    2074             : 
    2075             : /*
    2076             :  * Create and return the iterator for the given radix tree.
    2077             :  *
    2078             :  * Taking a lock in shared mode during the iteration is the caller's
    2079             :  * responsibility.
    2080             :  */
    2081             : RT_SCOPE    RT_ITER *
    2082         980 : RT_BEGIN_ITERATE(RT_RADIX_TREE * tree)
    2083             : {
    2084             :     RT_ITER    *iter;
    2085             :     RT_CHILD_PTR root;
    2086             : 
    2087         980 :     iter = (RT_ITER *) MemoryContextAllocZero(tree->iter_context,
    2088             :                                               sizeof(RT_ITER));
    2089         980 :     iter->tree = tree;
    2090             : 
    2091             :     Assert(RT_PTR_ALLOC_IS_VALID(tree->ctl->root));
    2092         980 :     root.alloc = iter->tree->ctl->root;
    2093         980 :     RT_PTR_SET_LOCAL(tree, &root);
    2094             : 
    2095         980 :     iter->top_level = iter->tree->ctl->start_shift / RT_SPAN;
    2096             : 
    2097             :     /* Set the root to start */
    2098         980 :     iter->cur_level = iter->top_level;
    2099         980 :     iter->node_iters[iter->cur_level].node = root;
    2100         980 :     iter->node_iters[iter->cur_level].idx = 0;
    2101             : 
    2102         980 :     return iter;
    2103             : }
    2104             : 
    2105             : /*
    2106             :  * Scan the inner node and return the next child pointer if one exists, otherwise
    2107             :  * return NULL.
    2108             :  */
    2109             : static inline RT_PTR_ALLOC *
    2110      250652 : RT_NODE_ITERATE_NEXT(RT_ITER * iter, int level)
    2111             : {
    2112      250652 :     uint8       key_chunk = 0;
    2113             :     RT_NODE_ITER *node_iter;
    2114             :     RT_CHILD_PTR node;
    2115      250652 :     RT_PTR_ALLOC *slot = NULL;
    2116             : 
    2117             : #ifdef RT_SHMEM
    2118             :     Assert(iter->tree->ctl->magic == RT_RADIX_TREE_MAGIC);
    2119             : #endif
    2120             : 
    2121      250652 :     node_iter = &(iter->node_iters[level]);
    2122      250652 :     node = node_iter->node;
    2123             : 
    2124             :     Assert(node.local != NULL);
    2125             : 
    2126      250652 :     switch ((node.local)->kind)
    2127             :     {
    2128       32876 :         case RT_NODE_KIND_4:
    2129             :             {
    2130       32876 :                 RT_NODE_4  *n4 = (RT_NODE_4 *) (node.local);
    2131             : 
    2132       32876 :                 if (node_iter->idx >= n4->base.count)
    2133       16140 :                     return NULL;
    2134             : 
    2135       16736 :                 slot = &n4->children[node_iter->idx];
    2136       16736 :                 key_chunk = n4->chunks[node_iter->idx];
    2137       16736 :                 node_iter->idx++;
    2138       16736 :                 break;
    2139             :             }
    2140        5716 :         case RT_NODE_KIND_16:
    2141             :             {
    2142        5716 :                 RT_NODE_16 *n16 = (RT_NODE_16 *) (node.local);
    2143             : 
    2144        5716 :                 if (node_iter->idx >= n16->base.count)
    2145         298 :                     return NULL;
    2146             : 
    2147        5418 :                 slot = &n16->children[node_iter->idx];
    2148        5418 :                 key_chunk = n16->chunks[node_iter->idx];
    2149        5418 :                 node_iter->idx++;
    2150        5418 :                 break;
    2151             :             }
    2152      188562 :         case RT_NODE_KIND_48:
    2153             :             {
    2154      188562 :                 RT_NODE_48 *n48 = (RT_NODE_48 *) (node.local);
    2155             :                 int         chunk;
    2156             : 
    2157     1059024 :                 for (chunk = node_iter->idx; chunk < RT_NODE_MAX_SLOTS; chunk++)
    2158             :                 {
    2159     1054908 :                     if (RT_NODE_48_IS_CHUNK_USED(n48, chunk))
    2160      184446 :                         break;
    2161             :                 }
    2162             : 
    2163      188562 :                 if (chunk >= RT_NODE_MAX_SLOTS)
    2164        4116 :                     return NULL;
    2165             : 
    2166      184446 :                 slot = RT_NODE_48_GET_CHILD(n48, chunk);
    2167             : 
    2168      184446 :                 key_chunk = chunk;
    2169      184446 :                 node_iter->idx = chunk + 1;
    2170      184446 :                 break;
    2171             :             }
    2172       23498 :         case RT_NODE_KIND_256:
    2173             :             {
    2174       23498 :                 RT_NODE_256 *n256 = (RT_NODE_256 *) (node.local);
    2175             :                 int         chunk;
    2176             : 
    2177       31340 :                 for (chunk = node_iter->idx; chunk < RT_NODE_MAX_SLOTS; chunk++)
    2178             :                 {
    2179       31232 :                     if (RT_NODE_256_IS_CHUNK_USED(n256, chunk))
    2180       23390 :                         break;
    2181             :                 }
    2182             : 
    2183       23498 :                 if (chunk >= RT_NODE_MAX_SLOTS)
    2184         108 :                     return NULL;
    2185             : 
    2186       23390 :                 slot = RT_NODE_256_GET_CHILD(n256, chunk);
    2187             : 
    2188       23390 :                 key_chunk = chunk;
    2189       23390 :                 node_iter->idx = chunk + 1;
    2190       23390 :                 break;
    2191             :             }
    2192             :     }
    2193             : 
    2194             :     /* Update the key */
    2195      229990 :     iter->key &= ~(((uint64) RT_CHUNK_MASK) << (level * RT_SPAN));
    2196      229990 :     iter->key |= (((uint64) key_chunk) << (level * RT_SPAN));
    2197             : 
    2198      229990 :     return slot;
    2199             : }
    2200             : 
    2201             : /*
    2202             :  * Return pointer to value and set key_p as long as there is a key.  Otherwise
    2203             :  * return NULL.
    2204             :  */
    2205             : RT_SCOPE    RT_VALUE_TYPE *
    2206      210998 : RT_ITERATE_NEXT(RT_ITER * iter, uint64 *key_p)
    2207             : {
    2208      210998 :     RT_PTR_ALLOC *slot = NULL;
    2209             : 
    2210      251570 :     while (iter->cur_level <= iter->top_level)
    2211             :     {
    2212             :         RT_CHILD_PTR node;
    2213             : 
    2214      250652 :         slot = RT_NODE_ITERATE_NEXT(iter, iter->cur_level);
    2215             : 
    2216      250652 :         if (iter->cur_level == 0 && slot != NULL)
    2217             :         {
    2218             :             /* Found a value at the leaf node */
    2219      210080 :             *key_p = iter->key;
    2220      210080 :             node.alloc = *slot;
    2221             : 
    2222      210080 :             if (RT_CHILDPTR_IS_VALUE(*slot))
    2223      210080 :                 return (RT_VALUE_TYPE *) slot;
    2224             :             else
    2225             :             {
    2226       20146 :                 RT_PTR_SET_LOCAL(iter->tree, &node);
    2227       20146 :                 return (RT_VALUE_TYPE *) node.local;
    2228             :             }
    2229             :         }
    2230             : 
    2231       40572 :         if (slot != NULL)
    2232             :         {
    2233             :             /* Found the child slot, move down the tree */
    2234       19910 :             node.alloc = *slot;
    2235       19910 :             RT_PTR_SET_LOCAL(iter->tree, &node);
    2236             : 
    2237       19910 :             iter->cur_level--;
    2238       19910 :             iter->node_iters[iter->cur_level].node = node;
    2239       19910 :             iter->node_iters[iter->cur_level].idx = 0;
    2240             :         }
    2241             :         else
    2242             :         {
    2243             :             /* Not found the child slot, move up the tree */
    2244       20662 :             iter->cur_level++;
    2245             :         }
    2246             :     }
    2247             : 
    2248             :     /* We've visited all nodes, so the iteration finished */
    2249         918 :     return NULL;
    2250             : }
    2251             : 
    2252             : /*
    2253             :  * Terminate the iteration. The caller is responsible for releasing any locks.
    2254             :  */
    2255             : RT_SCOPE void
    2256         980 : RT_END_ITERATE(RT_ITER * iter)
    2257             : {
    2258         980 :     pfree(iter);
    2259         980 : }
    2260             : 
    2261             : /***************** DELETION *****************/
    2262             : 
    2263             : #ifdef RT_USE_DELETE
    2264             : 
    2265             : /* Delete the element at "deletepos" */
    2266             : static inline void
    2267       43934 : RT_SHIFT_ARRAYS_AND_DELETE(uint8 *chunks, RT_PTR_ALLOC * children, int count, int deletepos)
    2268             : {
    2269             :     /*
    2270             :      * This is basically a memmove, but written in a simple loop for speed on
    2271             :      * small inputs.
    2272             :      */
    2273      197720 :     for (int i = deletepos; i < count - 1; i++)
    2274             :     {
    2275             :         /* workaround for https://gcc.gnu.org/bugzilla/show_bug.cgi?id=101481 */
    2276             : #ifdef __GNUC__
    2277      153786 :         __asm__("");
    2278             : #endif
    2279      153786 :         chunks[i] = chunks[i + 1];
    2280      153786 :         children[i] = children[i + 1];
    2281             :     }
    2282       43934 : }
    2283             : 
    2284             : /*
    2285             :  * Copy both chunk and slot arrays into the right
    2286             :  * place. The element at "deletepos" is deleted by skipping it.
    2287             :  */
    2288             : static inline void
    2289        4162 : RT_COPY_ARRAYS_AND_DELETE(uint8 *dst_chunks, RT_PTR_ALLOC * dst_children,
    2290             :                           uint8 *src_chunks, RT_PTR_ALLOC * src_children,
    2291             :                           int count, int deletepos)
    2292             : {
    2293       16648 :     for (int i = 0; i < count - 1; i++)
    2294             :     {
    2295             :         /*
    2296             :          * use a branch-free computation to skip the index of the deleted
    2297             :          * element
    2298             :          */
    2299       12486 :         int         sourceidx = i + (i >= deletepos);
    2300       12486 :         int         destidx = i;
    2301             : 
    2302       12486 :         dst_chunks[destidx] = src_chunks[sourceidx];
    2303       12486 :         dst_children[destidx] = src_children[sourceidx];
    2304             :     }
    2305        4162 : }
    2306             : 
    2307             : /*
    2308             :  * Note: While all node-growing functions are called to perform an insertion
    2309             :  * when no more space is available, shrinking is not a hard-and-fast requirement.
    2310             :  * When shrinking nodes, we generally wait until the count is about 3/4 of
    2311             :  * the next lower node's fanout. This prevents ping-ponging between different
    2312             :  * node sizes.
    2313             :  *
    2314             :  * Some shrinking functions delete first and then shrink, either because we
    2315             :  * must or because it's fast and simple that way. Sometimes it's faster to
    2316             :  * delete while shrinking.
    2317             :  */
    2318             : 
    2319             : /*
    2320             :  * Move contents of a node256 to a node48. Any deletion should have happened
    2321             :  * in the caller.
    2322             :  */
    2323             : static void pg_noinline
    2324          38 : RT_SHRINK_NODE_256(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, RT_CHILD_PTR node, uint8 chunk)
    2325             : {
    2326          38 :     RT_NODE_256 *n256 = (RT_NODE_256 *) node.local;
    2327             :     RT_CHILD_PTR newnode;
    2328             :     RT_NODE_48 *new48;
    2329          38 :     int         slot_idx = 0;
    2330             : 
    2331             :     /* initialize new node */
    2332          38 :     newnode = RT_ALLOC_NODE(tree, RT_NODE_KIND_48, RT_CLASS_48);
    2333          38 :     new48 = (RT_NODE_48 *) newnode.local;
    2334             : 
    2335             :     /* copy over the entries */
    2336          38 :     RT_COPY_COMMON(newnode, node);
    2337        9766 :     for (int i = 0; i < RT_NODE_MAX_SLOTS; i++)
    2338             :     {
    2339        9728 :         if (RT_NODE_256_IS_CHUNK_USED(n256, i))
    2340             :         {
    2341        1824 :             new48->slot_idxs[i] = slot_idx;
    2342        1824 :             new48->children[slot_idx] = n256->children[i];
    2343        1824 :             slot_idx++;
    2344             :         }
    2345             :     }
    2346             : 
    2347             :     /*
    2348             :      * Since we just copied a dense array, we can fill "isset" using a single
    2349             :      * store, provided the length of that array is at most the number of bits
    2350             :      * in a bitmapword.
    2351             :      */
    2352             :     Assert(n256->base.count <= BITS_PER_BITMAPWORD);
    2353          38 :     new48->isset[0] = (bitmapword) (((uint64) 1 << n256->base.count) - 1);
    2354             : 
    2355             :     /* free old node and update reference in parent */
    2356          38 :     *parent_slot = newnode.alloc;
    2357          38 :     RT_FREE_NODE(tree, node);
    2358          38 : }
    2359             : 
    2360             : static inline void
    2361        9080 : RT_REMOVE_CHILD_256(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, RT_CHILD_PTR node, uint8 chunk)
    2362             : {
    2363             :     int         shrink_threshold;
    2364        9080 :     RT_NODE_256 *n256 = (RT_NODE_256 *) node.local;
    2365        9080 :     int         idx = RT_BM_IDX(chunk);
    2366        9080 :     int         bitnum = RT_BM_BIT(chunk);
    2367             : 
    2368             :     /* Mark the slot free for "chunk" */
    2369        9080 :     n256->isset[idx] &= ~((bitmapword) 1 << bitnum);
    2370             : 
    2371        9080 :     n256->base.count--;
    2372             : 
    2373             :     /*
    2374             :      * A full node256 will have a count of zero because of overflow, so we
    2375             :      * delete first before checking the shrink threshold.
    2376             :      */
    2377             :     Assert(n256->base.count > 0);
    2378             : 
    2379             :     /* This simplifies RT_SHRINK_NODE_256() */
    2380        9080 :     shrink_threshold = BITS_PER_BITMAPWORD;
    2381        9080 :     shrink_threshold = Min(RT_FANOUT_48 / 4 * 3, shrink_threshold);
    2382             : 
    2383        9080 :     if (n256->base.count <= shrink_threshold)
    2384          38 :         RT_SHRINK_NODE_256(tree, parent_slot, node, chunk);
    2385        9080 : }
    2386             : 
    2387             : /*
    2388             :  * Move contents of a node48 to a node16. Any deletion should have happened
    2389             :  * in the caller.
    2390             :  */
    2391             : static void pg_noinline
    2392        4054 : RT_SHRINK_NODE_48(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, RT_CHILD_PTR node, uint8 chunk)
    2393             : {
    2394        4054 :     RT_NODE_48 *n48 = (RT_NODE_48 *) (node.local);
    2395             :     RT_CHILD_PTR newnode;
    2396             :     RT_NODE_16 *new16;
    2397        4054 :     int         destidx = 0;
    2398             : 
    2399             :     /*
    2400             :      * Initialize new node. For now we skip the larger node16 size class for
    2401             :      * simplicity.
    2402             :      */
    2403        4054 :     newnode = RT_ALLOC_NODE(tree, RT_NODE_KIND_16, RT_CLASS_16_LO);
    2404        4054 :     new16 = (RT_NODE_16 *) newnode.local;
    2405             : 
    2406             :     /* copy over all existing entries */
    2407        4054 :     RT_COPY_COMMON(newnode, node);
    2408     1041878 :     for (int chunk = 0; chunk < RT_NODE_MAX_SLOTS; chunk++)
    2409             :     {
    2410     1037824 :         if (n48->slot_idxs[chunk] != RT_INVALID_SLOT_IDX)
    2411             :         {
    2412       48648 :             new16->chunks[destidx] = chunk;
    2413       48648 :             new16->children[destidx] = n48->children[n48->slot_idxs[chunk]];
    2414       48648 :             destidx++;
    2415             :         }
    2416             :     }
    2417             : 
    2418             :     Assert(destidx < new16->base.fanout);
    2419             : 
    2420        4054 :     RT_VERIFY_NODE((RT_NODE *) new16);
    2421             : 
    2422             :     /* free old node and update reference in parent */
    2423        4054 :     *parent_slot = newnode.alloc;
    2424        4054 :     RT_FREE_NODE(tree, node);
    2425        4054 : }
    2426             : 
    2427             : static inline void
    2428      133948 : RT_REMOVE_CHILD_48(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, RT_CHILD_PTR node, uint8 chunk)
    2429             : {
    2430      133948 :     RT_NODE_48 *n48 = (RT_NODE_48 *) node.local;
    2431      133948 :     int         deletepos = n48->slot_idxs[chunk];
    2432             : 
    2433             :     /* For now we skip the larger node16 size class for simplicity */
    2434      133948 :     int         shrink_threshold = RT_FANOUT_16_LO / 4 * 3;
    2435             :     int         idx;
    2436             :     int         bitnum;
    2437             : 
    2438             :     Assert(deletepos != RT_INVALID_SLOT_IDX);
    2439             : 
    2440      133948 :     idx = RT_BM_IDX(deletepos);
    2441      133948 :     bitnum = RT_BM_BIT(deletepos);
    2442      133948 :     n48->isset[idx] &= ~((bitmapword) 1 << bitnum);
    2443      133948 :     n48->slot_idxs[chunk] = RT_INVALID_SLOT_IDX;
    2444             : 
    2445      133948 :     n48->base.count--;
    2446             : 
    2447             :     /*
    2448             :      * To keep shrinking simple, do it after deleting, which is fast for
    2449             :      * node48 anyway.
    2450             :      */
    2451      133948 :     if (n48->base.count <= shrink_threshold)
    2452        4054 :         RT_SHRINK_NODE_48(tree, parent_slot, node, chunk);
    2453      133948 : }
    2454             : 
    2455             : /*
    2456             :  * Move contents of a node16 to a node4, and delete the one at "deletepos".
    2457             :  * By deleting as we move, we can avoid memmove operations in the new
    2458             :  * node.
    2459             :  */
    2460             : static void pg_noinline
    2461        4162 : RT_SHRINK_NODE_16(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, RT_CHILD_PTR node, uint8 deletepos)
    2462             : {
    2463        4162 :     RT_NODE_16 *n16 = (RT_NODE_16 *) (node.local);
    2464             :     RT_CHILD_PTR newnode;
    2465             :     RT_NODE_4  *new4;
    2466             : 
    2467             :     /* initialize new node */
    2468        4162 :     newnode = RT_ALLOC_NODE(tree, RT_NODE_KIND_4, RT_CLASS_4);
    2469        4162 :     new4 = (RT_NODE_4 *) newnode.local;
    2470             : 
    2471             :     /* copy over existing entries, except for the one at "deletepos" */
    2472        4162 :     RT_COPY_COMMON(newnode, node);
    2473        4162 :     RT_COPY_ARRAYS_AND_DELETE(new4->chunks, new4->children,
    2474        4162 :                               n16->chunks, n16->children,
    2475        4162 :                               n16->base.count, deletepos);
    2476             : 
    2477        4162 :     new4->base.count--;
    2478        4162 :     RT_VERIFY_NODE((RT_NODE *) new4);
    2479             : 
    2480             :     /* free old node and update reference in parent */
    2481        4162 :     *parent_slot = newnode.alloc;
    2482        4162 :     RT_FREE_NODE(tree, node);
    2483        4162 : }
    2484             : 
    2485             : static inline void
    2486       39736 : RT_REMOVE_CHILD_16(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, RT_CHILD_PTR node, uint8 chunk, RT_PTR_ALLOC * slot)
    2487             : {
    2488       39736 :     RT_NODE_16 *n16 = (RT_NODE_16 *) node.local;
    2489       39736 :     int         deletepos = slot - n16->children;
    2490             : 
    2491             :     /*
    2492             :      * When shrinking to node4, 4 is hard-coded. After shrinking, the new node
    2493             :      * will end up with 3 elements and 3 is the largest count where linear
    2494             :      * search is faster than SIMD, at least on x86-64.
    2495             :      */
    2496       39736 :     if (n16->base.count <= 4)
    2497             :     {
    2498        4162 :         RT_SHRINK_NODE_16(tree, parent_slot, node, deletepos);
    2499        4162 :         return;
    2500             :     }
    2501             : 
    2502             :     Assert(deletepos >= 0);
    2503             :     Assert(n16->chunks[deletepos] == chunk);
    2504             : 
    2505       35574 :     RT_SHIFT_ARRAYS_AND_DELETE(n16->chunks, n16->children,
    2506       35574 :                                n16->base.count, deletepos);
    2507       35574 :     n16->base.count--;
    2508             : }
    2509             : 
    2510             : static inline void
    2511       39862 : RT_REMOVE_CHILD_4(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, RT_CHILD_PTR node, uint8 chunk, RT_PTR_ALLOC * slot)
    2512             : {
    2513       39862 :     RT_NODE_4  *n4 = (RT_NODE_4 *) node.local;
    2514             : 
    2515       39862 :     if (n4->base.count == 1)
    2516             :     {
    2517             :         Assert(n4->chunks[0] == chunk);
    2518             : 
    2519             :         /*
    2520             :          * If we're deleting the last entry from the root child node don't
    2521             :          * free it, but mark both the tree and the root child node empty. That
    2522             :          * way, RT_SET can assume it exists.
    2523             :          */
    2524       31502 :         if (parent_slot == &tree->ctl->root)
    2525             :         {
    2526          62 :             n4->base.count = 0;
    2527          62 :             tree->ctl->start_shift = 0;
    2528          62 :             tree->ctl->max_val = RT_SHIFT_GET_MAX_VAL(0);
    2529             :         }
    2530             :         else
    2531             :         {
    2532             :             /*
    2533             :              * Deleting last entry, so just free the entire node.
    2534             :              * RT_DELETE_RECURSIVE has already freed the value and lower-level
    2535             :              * children.
    2536             :              */
    2537       31440 :             RT_FREE_NODE(tree, node);
    2538             : 
    2539             :             /*
    2540             :              * Also null out the parent's slot -- this tells the next higher
    2541             :              * level to delete its child pointer
    2542             :              */
    2543       31440 :             *parent_slot = RT_INVALID_PTR_ALLOC;
    2544             :         }
    2545             :     }
    2546             :     else
    2547             :     {
    2548        8360 :         int         deletepos = slot - n4->children;
    2549             : 
    2550             :         Assert(deletepos >= 0);
    2551             :         Assert(n4->chunks[deletepos] == chunk);
    2552             : 
    2553        8360 :         RT_SHIFT_ARRAYS_AND_DELETE(n4->chunks, n4->children,
    2554        8360 :                                    n4->base.count, deletepos);
    2555             : 
    2556        8360 :         n4->base.count--;
    2557             :     }
    2558       39862 : }
    2559             : 
    2560             : /*
    2561             :  * Delete the child pointer corresponding to "key" in the given node.
    2562             :  */
    2563             : static inline void
    2564      222626 : RT_NODE_DELETE(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, RT_CHILD_PTR node, uint8 chunk, RT_PTR_ALLOC * slot)
    2565             : {
    2566      222626 :     switch ((node.local)->kind)
    2567             :     {
    2568       39862 :         case RT_NODE_KIND_4:
    2569             :             {
    2570       39862 :                 RT_REMOVE_CHILD_4(tree, parent_slot, node, chunk, slot);
    2571       39862 :                 return;
    2572             :             }
    2573       39736 :         case RT_NODE_KIND_16:
    2574             :             {
    2575       39736 :                 RT_REMOVE_CHILD_16(tree, parent_slot, node, chunk, slot);
    2576       39736 :                 return;
    2577             :             }
    2578      133948 :         case RT_NODE_KIND_48:
    2579             :             {
    2580      133948 :                 RT_REMOVE_CHILD_48(tree, parent_slot, node, chunk);
    2581      133948 :                 return;
    2582             :             }
    2583        9080 :         case RT_NODE_KIND_256:
    2584             :             {
    2585        9080 :                 RT_REMOVE_CHILD_256(tree, parent_slot, node, chunk);
    2586        9080 :                 return;
    2587             :             }
    2588           0 :         default:
    2589           0 :             pg_unreachable();
    2590             :     }
    2591             : }
    2592             : 
    2593             : /* workhorse for RT_DELETE */
    2594             : static bool
    2595      830432 : RT_DELETE_RECURSIVE(RT_RADIX_TREE * tree, RT_PTR_ALLOC * parent_slot, uint64 key, int shift)
    2596             : {
    2597             :     RT_PTR_ALLOC *slot;
    2598             :     RT_CHILD_PTR node;
    2599      830432 :     uint8       chunk = RT_GET_KEY_CHUNK(key, shift);
    2600             : 
    2601      830432 :     node.alloc = *parent_slot;
    2602      830432 :     RT_PTR_SET_LOCAL(tree, &node);
    2603      830432 :     slot = RT_NODE_SEARCH(node.local, chunk);
    2604             : 
    2605      830432 :     if (slot == NULL)
    2606       17528 :         return false;
    2607             : 
    2608      812904 :     if (shift == 0)
    2609             :     {
    2610      191186 :         if (!RT_CHILDPTR_IS_VALUE(*slot))
    2611           0 :             RT_FREE_LEAF(tree, *slot);
    2612             : 
    2613      191186 :         RT_NODE_DELETE(tree, parent_slot, node, chunk, slot);
    2614      191186 :         return true;
    2615             :     }
    2616             :     else
    2617             :     {
    2618             :         bool        deleted;
    2619             : 
    2620      621718 :         deleted = RT_DELETE_RECURSIVE(tree, slot, key, shift - RT_SPAN);
    2621             : 
    2622             :         /* Child node was freed, so delete its slot now */
    2623      621718 :         if (*slot == RT_INVALID_PTR_ALLOC)
    2624             :         {
    2625             :             Assert(deleted);
    2626       31440 :             RT_NODE_DELETE(tree, parent_slot, node, chunk, slot);
    2627             :         }
    2628             : 
    2629      621718 :         return deleted;
    2630             :     }
    2631             : }
    2632             : 
    2633             : /*
    2634             :  * Delete the given key from the radix tree. If the key is found delete it
    2635             :  * and return true, otherwise do nothing and return false.
    2636             :  *
    2637             :  * Taking a lock in exclusive mode is the caller's responsibility.
    2638             :  */
    2639             : RT_SCOPE bool
    2640      208714 : RT_DELETE(RT_RADIX_TREE * tree, uint64 key)
    2641             : {
    2642             :     bool        deleted;
    2643             : 
    2644             : #ifdef RT_SHMEM
    2645             :     Assert(tree->ctl->magic == RT_RADIX_TREE_MAGIC);
    2646             : #endif
    2647             : 
    2648      208714 :     if (key > tree->ctl->max_val)
    2649           0 :         return false;
    2650             : 
    2651             :     Assert(RT_PTR_ALLOC_IS_VALID(tree->ctl->root));
    2652      208714 :     deleted = RT_DELETE_RECURSIVE(tree, &tree->ctl->root,
    2653      208714 :                                   key, tree->ctl->start_shift);
    2654             : 
    2655             :     /* Found the key to delete. Update the statistics */
    2656      208714 :     if (deleted)
    2657             :     {
    2658      191186 :         tree->ctl->num_keys--;
    2659             :         Assert(tree->ctl->num_keys >= 0);
    2660             :     }
    2661             : 
    2662      208714 :     return deleted;
    2663             : }
    2664             : 
    2665             : #endif                          /* RT_USE_DELETE */
    2666             : 
    2667             : /***************** UTILITY FUNCTIONS *****************/
    2668             : 
    2669             : /*
    2670             :  * Return the statistics of the amount of memory used by the radix tree.
    2671             :  *
    2672             :  * Since dsa_get_total_size() does appropriate locking, the caller doesn't
    2673             :  * need to take a lock.
    2674             :  */
    2675             : RT_SCOPE uint64
    2676      114082 : RT_MEMORY_USAGE(RT_RADIX_TREE * tree)
    2677             : {
    2678      114082 :     size_t      total = 0;
    2679             : 
    2680             : #ifdef RT_SHMEM
    2681             :     Assert(tree->ctl->magic == RT_RADIX_TREE_MAGIC);
    2682        2288 :     total = dsa_get_total_size(tree->dsa);
    2683             : #else
    2684      111794 :     total = MemoryContextMemAllocated(tree->context, true);
    2685             : #endif
    2686             : 
    2687      114082 :     return total;
    2688             : }
    2689             : 
    2690             : /*
    2691             :  * Perform some sanity checks on the given node.
    2692             :  */
    2693             : static void
    2694      222760 : RT_VERIFY_NODE(RT_NODE * node)
    2695             : {
    2696             : #ifdef USE_ASSERT_CHECKING
    2697             : 
    2698             :     switch (node->kind)
    2699             :     {
    2700             :         case RT_NODE_KIND_4:
    2701             :             {
    2702             :                 RT_NODE_4  *n4 = (RT_NODE_4 *) node;
    2703             : 
    2704             :                 /* RT_DUMP_NODE(node); */
    2705             : 
    2706             :                 for (int i = 1; i < n4->base.count; i++)
    2707             :                     Assert(n4->chunks[i - 1] < n4->chunks[i]);
    2708             : 
    2709             :                 break;
    2710             :             }
    2711             :         case RT_NODE_KIND_16:
    2712             :             {
    2713             :                 RT_NODE_16 *n16 = (RT_NODE_16 *) node;
    2714             : 
    2715             :                 /* RT_DUMP_NODE(node); */
    2716             : 
    2717             :                 for (int i = 1; i < n16->base.count; i++)
    2718             :                     Assert(n16->chunks[i - 1] < n16->chunks[i]);
    2719             : 
    2720             :                 break;
    2721             :             }
    2722             :         case RT_NODE_KIND_48:
    2723             :             {
    2724             :                 RT_NODE_48 *n48 = (RT_NODE_48 *) node;
    2725             :                 int         cnt = 0;
    2726             : 
    2727             :                 /* RT_DUMP_NODE(node); */
    2728             : 
    2729             :                 for (int i = 0; i < RT_NODE_MAX_SLOTS; i++)
    2730             :                 {
    2731             :                     uint8       slot = n48->slot_idxs[i];
    2732             :                     int         idx = RT_BM_IDX(slot);
    2733             :                     int         bitnum = RT_BM_BIT(slot);
    2734             : 
    2735             :                     if (!RT_NODE_48_IS_CHUNK_USED(n48, i))
    2736             :                         continue;
    2737             : 
    2738             :                     /* Check if the corresponding slot is used */
    2739             :                     Assert(slot < node->fanout);
    2740             :                     Assert((n48->isset[idx] & ((bitmapword) 1 << bitnum)) != 0);
    2741             : 
    2742             :                     cnt++;
    2743             :                 }
    2744             : 
    2745             :                 Assert(n48->base.count == cnt);
    2746             : 
    2747             :                 break;
    2748             :             }
    2749             :         case RT_NODE_KIND_256:
    2750             :             {
    2751             :                 RT_NODE_256 *n256 = (RT_NODE_256 *) node;
    2752             :                 int         cnt = 0;
    2753             : 
    2754             :                 /* RT_DUMP_NODE(node); */
    2755             : 
    2756             :                 for (int i = 0; i < RT_BM_IDX(RT_NODE_MAX_SLOTS); i++)
    2757             :                     cnt += bmw_popcount(n256->isset[i]);
    2758             : 
    2759             :                 /*
    2760             :                  * Check if the number of used chunk matches, accounting for
    2761             :                  * overflow
    2762             :                  */
    2763             :                 if (cnt == RT_FANOUT_256)
    2764             :                     Assert(n256->base.count == 0);
    2765             :                 else
    2766             :                     Assert(n256->base.count == cnt);
    2767             : 
    2768             :                 break;
    2769             :             }
    2770             :     }
    2771             : #endif
    2772      222760 : }
    2773             : 
    2774             : /***************** DEBUG FUNCTIONS *****************/
    2775             : 
    2776             : #ifdef RT_DEBUG
    2777             : 
    2778             : /*
    2779             :  * Print out tree stats, some of which are only collected in debugging builds.
    2780             :  */
    2781             : RT_SCOPE void
    2782         122 : RT_STATS(RT_RADIX_TREE * tree)
    2783             : {
    2784         122 :     fprintf(stderr, "max_val = " UINT64_FORMAT "\n", tree->ctl->max_val);
    2785         122 :     fprintf(stderr, "num_keys = %lld\n", (long long) tree->ctl->num_keys);
    2786             : 
    2787             : #ifdef RT_SHMEM
    2788             :     fprintf(stderr, "handle = " DSA_POINTER_FORMAT "\n", tree->ctl->handle);
    2789             : #endif
    2790             : 
    2791         122 :     fprintf(stderr, "height = %d", tree->ctl->start_shift / RT_SPAN);
    2792             : 
    2793         732 :     for (int i = 0; i < RT_NUM_SIZE_CLASSES; i++)
    2794             :     {
    2795         610 :         RT_SIZE_CLASS_ELEM size_class = RT_SIZE_CLASS_INFO[i];
    2796             : 
    2797         610 :         fprintf(stderr, ", n%d = %lld", size_class.fanout, (long long) tree->ctl->num_nodes[i]);
    2798             :     }
    2799             : 
    2800         122 :     fprintf(stderr, ", leaves = %lld", (long long) tree->ctl->num_leaves);
    2801             : 
    2802         122 :     fprintf(stderr, "\n");
    2803         122 : }
    2804             : 
    2805             : /*
    2806             :  * Print out debugging information about the given node.
    2807             :  */
    2808             : static void
    2809             : pg_attribute_unused()
    2810           0 : RT_DUMP_NODE(RT_NODE * node)
    2811             : {
    2812             : #ifdef RT_SHMEM
    2813             : #define RT_CHILD_PTR_FORMAT DSA_POINTER_FORMAT
    2814             : #else
    2815             : #define RT_CHILD_PTR_FORMAT "%p"
    2816             : #endif
    2817             : 
    2818           0 :     fprintf(stderr, "kind %d, fanout %d, count %u\n",
    2819           0 :             (node->kind == RT_NODE_KIND_4) ? 4 :
    2820           0 :             (node->kind == RT_NODE_KIND_16) ? 16 :
    2821           0 :             (node->kind == RT_NODE_KIND_48) ? 48 : 256,
    2822           0 :             node->fanout == 0 ? 256 : node->fanout,
    2823           0 :             node->count == 0 ? 256 : node->count);
    2824             : 
    2825           0 :     switch (node->kind)
    2826             :     {
    2827           0 :         case RT_NODE_KIND_4:
    2828             :             {
    2829           0 :                 RT_NODE_4  *n4 = (RT_NODE_4 *) node;
    2830             : 
    2831           0 :                 fprintf(stderr, "chunks and slots:\n");
    2832           0 :                 for (int i = 0; i < n4->base.count; i++)
    2833             :                 {
    2834           0 :                     fprintf(stderr, "  [%d] chunk %x slot " RT_CHILD_PTR_FORMAT "\n",
    2835           0 :                             i, n4->chunks[i], n4->children[i]);
    2836             :                 }
    2837             : 
    2838           0 :                 break;
    2839             :             }
    2840           0 :         case RT_NODE_KIND_16:
    2841             :             {
    2842           0 :                 RT_NODE_16 *n16 = (RT_NODE_16 *) node;
    2843             : 
    2844           0 :                 fprintf(stderr, "chunks and slots:\n");
    2845           0 :                 for (int i = 0; i < n16->base.count; i++)
    2846             :                 {
    2847           0 :                     fprintf(stderr, "  [%d] chunk %x slot " RT_CHILD_PTR_FORMAT "\n",
    2848           0 :                             i, n16->chunks[i], n16->children[i]);
    2849             :                 }
    2850           0 :                 break;
    2851             :             }
    2852           0 :         case RT_NODE_KIND_48:
    2853             :             {
    2854           0 :                 RT_NODE_48 *n48 = (RT_NODE_48 *) node;
    2855           0 :                 char       *sep = "";
    2856             : 
    2857           0 :                 fprintf(stderr, "slot_idxs: \n");
    2858           0 :                 for (int chunk = 0; chunk < RT_NODE_MAX_SLOTS; chunk++)
    2859             :                 {
    2860           0 :                     if (!RT_NODE_48_IS_CHUNK_USED(n48, chunk))
    2861           0 :                         continue;
    2862             : 
    2863           0 :                     fprintf(stderr, "  idx[%d] = %d\n",
    2864           0 :                             chunk, n48->slot_idxs[chunk]);
    2865             :                 }
    2866             : 
    2867           0 :                 fprintf(stderr, "isset-bitmap: ");
    2868           0 :                 for (int i = 0; i < (RT_FANOUT_48_MAX / BITS_PER_BYTE); i++)
    2869             :                 {
    2870           0 :                     fprintf(stderr, "%s%x", sep, ((uint8 *) n48->isset)[i]);
    2871           0 :                     sep = " ";
    2872             :                 }
    2873           0 :                 fprintf(stderr, "\n");
    2874             : 
    2875           0 :                 fprintf(stderr, "chunks and slots:\n");
    2876           0 :                 for (int chunk = 0; chunk < RT_NODE_MAX_SLOTS; chunk++)
    2877             :                 {
    2878           0 :                     if (!RT_NODE_48_IS_CHUNK_USED(n48, chunk))
    2879           0 :                         continue;
    2880             : 
    2881           0 :                     fprintf(stderr, "  chunk %x slot " RT_CHILD_PTR_FORMAT "\n",
    2882             :                             chunk,
    2883           0 :                             *RT_NODE_48_GET_CHILD(n48, chunk));
    2884             :                 }
    2885           0 :                 break;
    2886             :             }
    2887           0 :         case RT_NODE_KIND_256:
    2888             :             {
    2889           0 :                 RT_NODE_256 *n256 = (RT_NODE_256 *) node;
    2890           0 :                 char       *sep = "";
    2891             : 
    2892           0 :                 fprintf(stderr, "isset-bitmap: ");
    2893           0 :                 for (int i = 0; i < (RT_FANOUT_256 / BITS_PER_BYTE); i++)
    2894             :                 {
    2895           0 :                     fprintf(stderr, "%s%x", sep, ((uint8 *) n256->isset)[i]);
    2896           0 :                     sep = " ";
    2897             :                 }
    2898           0 :                 fprintf(stderr, "\n");
    2899             : 
    2900           0 :                 fprintf(stderr, "chunks and slots:\n");
    2901           0 :                 for (int chunk = 0; chunk < RT_NODE_MAX_SLOTS; chunk++)
    2902             :                 {
    2903           0 :                     if (!RT_NODE_256_IS_CHUNK_USED(n256, chunk))
    2904           0 :                         continue;
    2905             : 
    2906           0 :                     fprintf(stderr, "  chunk %x slot " RT_CHILD_PTR_FORMAT "\n",
    2907             :                             chunk,
    2908           0 :                             *RT_NODE_256_GET_CHILD(n256, chunk));
    2909             :                 }
    2910           0 :                 break;
    2911             :             }
    2912             :     }
    2913           0 : }
    2914             : #endif                          /* RT_DEBUG */
    2915             : 
    2916             : #endif                          /* RT_DEFINE */
    2917             : 
    2918             : 
    2919             : /* undefine external parameters, so next radix tree can be defined */
    2920             : #undef RT_PREFIX
    2921             : #undef RT_SCOPE
    2922             : #undef RT_DECLARE
    2923             : #undef RT_DEFINE
    2924             : #undef RT_VALUE_TYPE
    2925             : #undef RT_VARLEN_VALUE_SIZE
    2926             : #undef RT_RUNTIME_EMBEDDABLE_VALUE
    2927             : #undef RT_SHMEM
    2928             : #undef RT_USE_DELETE
    2929             : #undef RT_DEBUG
    2930             : 
    2931             : /* locally declared macros */
    2932             : #undef RT_MAKE_PREFIX
    2933             : #undef RT_MAKE_NAME
    2934             : #undef RT_MAKE_NAME_
    2935             : #undef RT_STR
    2936             : #undef RT_STR_
    2937             : #undef RT_SPAN
    2938             : #undef RT_NODE_MAX_SLOTS
    2939             : #undef RT_CHUNK_MASK
    2940             : #undef RT_MAX_SHIFT
    2941             : #undef RT_MAX_LEVEL
    2942             : #undef RT_GET_KEY_CHUNK
    2943             : #undef RT_BM_IDX
    2944             : #undef RT_BM_BIT
    2945             : #undef RT_NODE_MUST_GROW
    2946             : #undef RT_NODE_KIND_COUNT
    2947             : #undef RT_NUM_SIZE_CLASSES
    2948             : #undef RT_INVALID_SLOT_IDX
    2949             : #undef RT_SLAB_BLOCK_SIZE
    2950             : #undef RT_RADIX_TREE_MAGIC
    2951             : #undef RT_CHILD_PTR_FORMAT
    2952             : 
    2953             : /* type declarations */
    2954             : #undef RT_RADIX_TREE
    2955             : #undef RT_RADIX_TREE_CONTROL
    2956             : #undef RT_CHILD_PTR
    2957             : #undef RT_PTR_ALLOC
    2958             : #undef RT_INVALID_PTR_ALLOC
    2959             : #undef RT_HANDLE
    2960             : #undef RT_ITER
    2961             : #undef RT_NODE
    2962             : #undef RT_NODE_ITER
    2963             : #undef RT_NODE_KIND_4
    2964             : #undef RT_NODE_KIND_16
    2965             : #undef RT_NODE_KIND_48
    2966             : #undef RT_NODE_KIND_256
    2967             : #undef RT_NODE_4
    2968             : #undef RT_NODE_16
    2969             : #undef RT_NODE_48
    2970             : #undef RT_NODE_256
    2971             : #undef RT_SIZE_CLASS
    2972             : #undef RT_SIZE_CLASS_ELEM
    2973             : #undef RT_SIZE_CLASS_INFO
    2974             : #undef RT_CLASS_4
    2975             : #undef RT_CLASS_16_LO
    2976             : #undef RT_CLASS_16_HI
    2977             : #undef RT_CLASS_48
    2978             : #undef RT_CLASS_256
    2979             : #undef RT_FANOUT_4
    2980             : #undef RT_FANOUT_4_MAX
    2981             : #undef RT_FANOUT_16_LO
    2982             : #undef RT_FANOUT_16_HI
    2983             : #undef RT_FANOUT_16_MAX
    2984             : #undef RT_FANOUT_48
    2985             : #undef RT_FANOUT_48_MAX
    2986             : #undef RT_FANOUT_256
    2987             : 
    2988             : /* function declarations */
    2989             : #undef RT_CREATE
    2990             : #undef RT_FREE
    2991             : #undef RT_ATTACH
    2992             : #undef RT_DETACH
    2993             : #undef RT_LOCK_EXCLUSIVE
    2994             : #undef RT_LOCK_SHARE
    2995             : #undef RT_UNLOCK
    2996             : #undef RT_GET_HANDLE
    2997             : #undef RT_FIND
    2998             : #undef RT_SET
    2999             : #undef RT_BEGIN_ITERATE
    3000             : #undef RT_ITERATE_NEXT
    3001             : #undef RT_END_ITERATE
    3002             : #undef RT_DELETE
    3003             : #undef RT_MEMORY_USAGE
    3004             : #undef RT_DUMP_NODE
    3005             : #undef RT_STATS
    3006             : 
    3007             : /* internal helper functions */
    3008             : #undef RT_GET_VALUE_SIZE
    3009             : #undef RT_VALUE_IS_EMBEDDABLE
    3010             : #undef RT_CHILDPTR_IS_VALUE
    3011             : #undef RT_GET_SLOT_RECURSIVE
    3012             : #undef RT_DELETE_RECURSIVE
    3013             : #undef RT_ALLOC_NODE
    3014             : #undef RT_ALLOC_LEAF
    3015             : #undef RT_FREE_NODE
    3016             : #undef RT_FREE_LEAF
    3017             : #undef RT_FREE_RECURSE
    3018             : #undef RT_EXTEND_UP
    3019             : #undef RT_EXTEND_DOWN
    3020             : #undef RT_COPY_COMMON
    3021             : #undef RT_PTR_SET_LOCAL
    3022             : #undef RT_PTR_ALLOC_IS_VALID
    3023             : #undef RT_NODE_16_SEARCH_EQ
    3024             : #undef RT_NODE_4_GET_INSERTPOS
    3025             : #undef RT_NODE_16_GET_INSERTPOS
    3026             : #undef RT_SHIFT_ARRAYS_FOR_INSERT
    3027             : #undef RT_SHIFT_ARRAYS_AND_DELETE
    3028             : #undef RT_COPY_ARRAYS_FOR_INSERT
    3029             : #undef RT_COPY_ARRAYS_AND_DELETE
    3030             : #undef RT_NODE_48_IS_CHUNK_USED
    3031             : #undef RT_NODE_48_GET_CHILD
    3032             : #undef RT_NODE_256_IS_CHUNK_USED
    3033             : #undef RT_NODE_256_GET_CHILD
    3034             : #undef RT_KEY_GET_SHIFT
    3035             : #undef RT_SHIFT_GET_MAX_VAL
    3036             : #undef RT_NODE_SEARCH
    3037             : #undef RT_ADD_CHILD_4
    3038             : #undef RT_ADD_CHILD_16
    3039             : #undef RT_ADD_CHILD_48
    3040             : #undef RT_ADD_CHILD_256
    3041             : #undef RT_GROW_NODE_4
    3042             : #undef RT_GROW_NODE_16
    3043             : #undef RT_GROW_NODE_48
    3044             : #undef RT_REMOVE_CHILD_4
    3045             : #undef RT_REMOVE_CHILD_16
    3046             : #undef RT_REMOVE_CHILD_48
    3047             : #undef RT_REMOVE_CHILD_256
    3048             : #undef RT_SHRINK_NODE_16
    3049             : #undef RT_SHRINK_NODE_48
    3050             : #undef RT_SHRINK_NODE_256
    3051             : #undef RT_NODE_DELETE
    3052             : #undef RT_NODE_INSERT
    3053             : #undef RT_NODE_ITERATE_NEXT
    3054             : #undef RT_VERIFY_NODE

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