1.\" $OpenBSD: tree.3,v 1.7 2002/06/12 01:09:20 provos Exp $ 2.\" 3.\" Copyright 2002 Niels Provos <provos@citi.umich.edu> 4.\" All rights reserved. 5.\" 6.\" Redistribution and use in source and binary forms, with or without 7.\" modification, are permitted provided that the following conditions 8.\" are met: 9.\" 1. Redistributions of source code must retain the above copyright 10.\" notice, this list of conditions and the following disclaimer. 11.\" 2. Redistributions in binary form must reproduce the above copyright 12.\" notice, this list of conditions and the following disclaimer in the 13.\" documentation and/or other materials provided with the distribution. 14.\" 3. All advertising materials mentioning features or use of this software 15.\" must display the following acknowledgement: 16.\" This product includes software developed by Niels Provos. 17.\" 4. The name of the author may not be used to endorse or promote products 18.\" derived from this software without specific prior written permission. 19.\" 20.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 21.\" IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 22.\" OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 23.\" IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 24.\" INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 25.\" NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 26.\" DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 27.\" THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 28.\" (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 29.\" THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 30.\" 31.\" $FreeBSD$ 32.\" 33.Dd May 8, 2019 34.Dt ARB 3 35.Os 36.Sh NAME 37.Nm ARB_PROTOTYPE , 38.Nm ARB_PROTOTYPE_STATIC , 39.Nm ARB_PROTOTYPE_INSERT , 40.Nm ARB_PROTOTYPE_INSERT_COLOR , 41.Nm ARB_PROTOTYPE_REMOVE , 42.Nm ARB_PROTOTYPE_REMOVE_COLOR , 43.Nm ARB_PROTOTYPE_FIND , 44.Nm ARB_PROTOTYPE_NFIND , 45.Nm ARB_PROTOTYPE_NEXT , 46.Nm ARB_PROTOTYPE_PREV , 47.Nm ARB_PROTOTYPE_MINMAX , 48.Nm ARB_GENERATE , 49.Nm ARB_GENERATE_STATIC , 50.Nm ARB_GENERATE_INSERT , 51.Nm ARB_GENERATE_INSERT_COLOR , 52.Nm ARB_GENERATE_REMOVE , 53.Nm ARB_GENERATE_REMOVE_COLOR , 54.Nm ARB_GENERATE_FIND , 55.Nm ARB_GENERATE_NFIND , 56.Nm ARB_GENERATE_NEXT , 57.Nm ARB_GENERATE_PREV , 58.Nm ARB_GENERATE_MINMAX , 59.Nm ARB8_ENTRY , 60.Nm ARB16_ENTRY , 61.Nm ARB32_ENTRY , 62.Nm ARB8_HEAD , 63.Nm ARB16_HEAD , 64.Nm ARB32_HEAD , 65.Nm ARB_ALLOCSIZE , 66.Nm ARB_INITIALIZER , 67.Nm ARB_ROOT , 68.Nm ARB_EMPTY , 69.Nm ARB_FULL , 70.Nm ARB_CURNODES , 71.Nm ARB_MAXNODES , 72.Nm ARB_NEXT , 73.Nm ARB_PREV , 74.Nm ARB_MIN , 75.Nm ARB_MAX , 76.Nm ARB_FIND , 77.Nm ARB_NFIND , 78.Nm ARB_LEFT , 79.Nm ARB_LEFTIDX , 80.Nm ARB_RIGHT , 81.Nm ARB_RIGHTIDX , 82.Nm ARB_PARENT , 83.Nm ARB_PARENTIDX , 84.Nm ARB_GETFREE , 85.Nm ARB_FREEIDX , 86.Nm ARB_FOREACH , 87.Nm ARB_FOREACH_FROM , 88.Nm ARB_FOREACH_SAFE , 89.Nm ARB_FOREACH_REVERSE , 90.Nm ARB_FOREACH_REVERSE_FROM , 91.Nm ARB_FOREACH_REVERSE_SAFE , 92.Nm ARB_INIT , 93.Nm ARB_INSERT , 94.Nm ARB_REMOVE 95.Nd "array-based red-black trees" 96.Sh SYNOPSIS 97.In sys/arb.h 98.Fn ARB_PROTOTYPE NAME TYPE FIELD CMP 99.Fn ARB_PROTOTYPE_STATIC NAME TYPE FIELD CMP 100.Fn ARB_PROTOTYPE_INSERT NAME TYPE ATTR 101.Fn ARB_PROTOTYPE_INSERT_COLOR NAME TYPE ATTR 102.Fn ARB_PROTOTYPE_REMOVE NAME TYPE ATTR 103.Fn ARB_PROTOTYPE_REMOVE_COLOR NAME TYPE ATTR 104.Fn ARB_PROTOTYPE_FIND NAME TYPE ATTR 105.Fn ARB_PROTOTYPE_NFIND NAME TYPE ATTR 106.Fn ARB_PROTOTYPE_NEXT NAME TYPE ATTR 107.Fn ARB_PROTOTYPE_PREV NAME TYPE ATTR 108.Fn ARB_PROTOTYPE_MINMAX NAME TYPE ATTR 109.Fn ARB_GENERATE NAME TYPE FIELD CMP 110.Fn ARB_GENERATE_STATIC NAME TYPE FIELD CMP 111.Fn ARB_GENERATE_INSERT NAME TYPE FIELD CMP ATTR 112.Fn ARB_GENERATE_INSERT_COLOR NAME TYPE FIELD ATTR 113.Fn ARB_GENERATE_REMOVE NAME TYPE FIELD ATTR 114.Fn ARB_GENERATE_REMOVE_COLOR NAME TYPE FIELD ATTR 115.Fn ARB_GENERATE_FIND NAME TYPE FIELD CMP ATTR 116.Fn ARB_GENERATE_NFIND NAME TYPE FIELD CMP ATTR 117.Fn ARB_GENERATE_NEXT NAME TYPE FIELD ATTR 118.Fn ARB_GENERATE_PREV NAME TYPE FIELD ATTR 119.Fn ARB_GENERATE_MINMAX NAME TYPE FIELD ATTR 120.Fn ARB<8|16|32>_ENTRY 121.Fn ARB<8|16|32>_HEAD HEADNAME TYPE 122.Ft "size_t" 123.Fn ARB_ALLOCSIZE "ARB_HEAD *head" "int<8|16|32>_t maxnodes" "struct TYPE *elm" 124.Fn ARB_INITIALIZER "ARB_HEAD *head" "int<8|16|32>_t maxnodes" 125.Ft "struct TYPE *" 126.Fn ARB_ROOT "ARB_HEAD *head" 127.Ft "bool" 128.Fn ARB_EMPTY "ARB_HEAD *head" 129.Ft "bool" 130.Fn ARB_FULL "ARB_HEAD *head" 131.Ft "int<8|16|32>_t" 132.Fn ARB_CURNODES "ARB_HEAD *head" 133.Ft "int<8|16|32>_t" 134.Fn ARB_MAXNODES "ARB_HEAD *head" 135.Ft "struct TYPE *" 136.Fn ARB_NEXT NAME "ARB_HEAD *head" "struct TYPE *elm" 137.Ft "struct TYPE *" 138.Fn ARB_PREV NAME "ARB_HEAD *head" "struct TYPE *elm" 139.Ft "struct TYPE *" 140.Fn ARB_MIN NAME "ARB_HEAD *head" 141.Ft "struct TYPE *" 142.Fn ARB_MAX NAME "ARB_HEAD *head" 143.Ft "struct TYPE *" 144.Fn ARB_FIND NAME "ARB_HEAD *head" "struct TYPE *elm" 145.Ft "struct TYPE *" 146.Fn ARB_NFIND NAME "ARB_HEAD *head" "struct TYPE *elm" 147.Ft "struct TYPE *" 148.Fn ARB_LEFT "struct TYPE *elm" "ARB_ENTRY NAME" 149.Ft "int<8|16|32>_t" 150.Fn ARB_LEFTIDX "struct TYPE *elm" "ARB_ENTRY NAME" 151.Ft "struct TYPE *" 152.Fn ARB_RIGHT "struct TYPE *elm" "ARB_ENTRY NAME" 153.Ft "int<8|16|32>_t" 154.Fn ARB_RIGHTIDX "struct TYPE *elm" "ARB_ENTRY NAME" 155.Ft "struct TYPE *" 156.Fn ARB_PARENT "struct TYPE *elm" "ARB_ENTRY NAME" 157.Ft "int<8|16|32>_t" 158.Fn ARB_PARENTIDX "struct TYPE *elm" "ARB_ENTRY NAME" 159.Ft "struct TYPE *" 160.Fn ARB_GETFREE "ARB_HEAD *head" "FIELD" 161.Ft "int<8|16|32>_t" 162.Fn ARB_FREEIDX "ARB_HEAD *head" 163.Fn ARB_FOREACH VARNAME NAME "ARB_HEAD *head" 164.Fn ARB_FOREACH_FROM "VARNAME" "NAME" "POS_VARNAME" 165.Fn ARB_FOREACH_SAFE "VARNAME" "NAME" "ARB_HEAD *head" "TEMP_VARNAME" 166.Fn ARB_FOREACH_REVERSE VARNAME NAME "ARB_HEAD *head" 167.Fn ARB_FOREACH_REVERSE_FROM "VARNAME" "NAME" "POS_VARNAME" 168.Fn ARB_FOREACH_REVERSE_SAFE "VARNAME" "NAME" "ARB_HEAD *head" "TEMP_VARNAME" 169.Ft void 170.Fn ARB_INIT "struct TYPE *elm" "FIELD" "ARB_HEAD *head" "int<8|16|32>_t maxnodes" 171.Ft "struct TYPE *" 172.Fn ARB_INSERT NAME "ARB_HEAD *head" "struct TYPE *elm" 173.Ft "struct TYPE *" 174.Fn ARB_REMOVE NAME "ARB_HEAD *head" "struct TYPE *elm" 175.Sh DESCRIPTION 176These macros define data structures for and array-based red-black trees. 177They use a single, continuous chunk of memory, and are useful 178e.g., when the tree needs to be transferred between userspace and kernel. 179.Pp 180In the macro definitions, 181.Fa TYPE 182is the name tag of a user defined structure that must contain a field of type 183.Vt ARB_ENTRY , 184named 185.Fa ENTRYNAME . 186The argument 187.Fa HEADNAME 188is the name tag of a user defined structure that must be declared 189using the 190.Fn ARB_HEAD 191macro. 192The argument 193.Fa NAME 194has to be a unique name prefix for every tree that is defined. 195.Pp 196The function prototypes are declared with 197.Fn ARB_PROTOTYPE , 198or 199.Fn ARB_PROTOTYPE_STATIC . 200The function bodies are generated with 201.Fn ARB_GENERATE , 202or 203.Fn ARB_GENERATE_STATIC . 204See the examples below for further explanation of how these macros are used. 205.Pp 206A red-black tree is a binary search tree with the node color as an 207extra attribute. 208It fulfills a set of conditions: 209.Bl -enum -offset indent 210.It 211Every search path from the root to a leaf consists of the same number of 212black nodes. 213.It 214Each red node (except for the root) has a black parent. 215.It 216Each leaf node is black. 217.El 218.Pp 219Every operation on a red-black tree is bounded as 220.Fn O "lg n" . 221The maximum height of a red-black tree is 222.Fn 2lg "n + 1" . 223.Pp 224.Fn ARB_* 225trees require entries to be allocated as an array, and uses array 226indices to link entries together. 227The maximum number of 228.Fn ARB_* 229tree entries is therefore constrained by the minimum of array size and choice of 230signed integer data type used to store array indices. 231Use 232.Fn ARB_ALLOCSIZE 233to compute the size of memory chunk to allocate. 234.Pp 235A red-black tree is headed by a structure defined by the 236.Fn ARB_HEAD 237macro. 238A 239structure is declared with either of the following: 240.Bd -ragged -offset indent 241.Fn ARB<8|16|32>_HEAD HEADNAME TYPE 242.Va head ; 243.Ed 244.Pp 245where 246.Fa HEADNAME 247is the name of the structure to be defined, and struct 248.Fa TYPE 249is the type of the elements to be inserted into the tree. 250.Pp 251The 252.Fn ARB_HEAD 253variant includes a suffix denoting the signed integer data type size 254.Pq in bits 255used to store array indices. 256For example, 257.Fn ARB_HEAD8 258creates a red-black tree head strucutre with 8-bit signed array indices capable 259of indexing up to 128 entries. 260.Pp 261The 262.Fn ARB_ENTRY 263macro declares a structure that allows elements to be connected in the tree. 264Similarly to the 265.Fn ARB<8|16|32>_HEAD 266macro, the 267.Fn ARB_ENTRY 268variant includes a suffix denoting the signed integer data type size 269.Pq in bits 270used to store array indices. 271Entries should use the same number of bits as the tree head structure they will 272be linked into. 273.Pp 274In order to use the functions that manipulate the tree structure, 275their prototypes need to be declared with the 276.Fn ARB_PROTOTYPE 277or 278.Fn ARB_PROTOTYPE_STATIC 279macro, 280where 281.Fa NAME 282is a unique identifier for this particular tree. 283The 284.Fa TYPE 285argument is the type of the structure that is being managed 286by the tree. 287The 288.Fa FIELD 289argument is the name of the element defined by 290.Fn ARB_ENTRY . 291Individual prototypes can be declared with 292.Fn ARB_PROTOTYPE_INSERT , 293.Fn ARB_PROTOTYPE_INSERT_COLOR , 294.Fn ARB_PROTOTYPE_REMOVE , 295.Fn ARB_PROTOTYPE_REMOVE_COLOR , 296.Fn ARB_PROTOTYPE_FIND , 297.Fn ARB_PROTOTYPE_NFIND , 298.Fn ARB_PROTOTYPE_NEXT , 299.Fn ARB_PROTOTYPE_PREV , 300and 301.Fn ARB_PROTOTYPE_MINMAX 302in case not all functions are required. 303The individual prototype macros expect 304.Fa NAME , 305.Fa TYPE , 306and 307.Fa ATTR 308arguments. 309The 310.Fa ATTR 311argument must be empty for global functions or 312.Fa static 313for static functions. 314.Pp 315The function bodies are generated with the 316.Fn ARB_GENERATE 317or 318.Fn ARB_GENERATE_STATIC 319macro. 320These macros take the same arguments as the 321.Fn ARB_PROTOTYPE 322and 323.Fn ARB_PROTOTYPE_STATIC 324macros, but should be used only once. 325As an alternative individual function bodies are generated with the 326.Fn ARB_GENERATE_INSERT , 327.Fn ARB_GENERATE_INSERT_COLOR , 328.Fn ARB_GENERATE_REMOVE , 329.Fn ARB_GENERATE_REMOVE_COLOR , 330.Fn ARB_GENERATE_FIND , 331.Fn ARB_GENERATE_NFIND , 332.Fn ARB_GENERATE_NEXT , 333.Fn ARB_GENERATE_PREV , 334and 335.Fn ARB_GENERATE_MINMAX 336macros. 337.Pp 338Finally, 339the 340.Fa CMP 341argument is the name of a function used to compare tree nodes 342with each other. 343The function takes two arguments of type 344.Vt "struct TYPE *" . 345If the first argument is smaller than the second, the function returns a 346value smaller than zero. 347If they are equal, the function returns zero. 348Otherwise, it should return a value greater than zero. 349The compare 350function defines the order of the tree elements. 351.Pp 352The 353.Fn ARB_INIT 354macro initializes the tree referenced by 355.Fa head , 356with the array length of 357.Fa maxnodes . 358.Pp 359The red-black tree can also be initialized statically by using the 360.Fn ARB_INITIALIZER 361macro: 362.Bd -ragged -offset indent 363.Fn ARB<8|16|32>_HEAD HEADNAME TYPE 364.Va head 365= 366.Fn ARB_INITIALIZER &head maxnodes ; 367.Ed 368.Pp 369The 370.Fn ARB_INSERT 371macro inserts the new element 372.Fa elm 373into the tree. 374.Pp 375The 376.Fn ARB_REMOVE 377macro removes the element 378.Fa elm 379from the tree pointed by 380.Fa head . 381.Pp 382The 383.Fn ARB_FIND 384and 385.Fn ARB_NFIND 386macros can be used to find a particular element in the tree. 387.Bd -literal -offset indent 388struct TYPE find, *res; 389find.key = 30; 390res = RB_FIND(NAME, head, &find); 391.Ed 392.Pp 393The 394.Fn ARB_ROOT , 395.Fn ARB_MIN , 396.Fn ARB_MAX , 397.Fn ARB_NEXT , 398and 399.Fn ARB_PREV 400macros can be used to traverse the tree: 401.Pp 402.Dl "for (np = RB_MIN(NAME, &head); np != NULL; np = RB_NEXT(NAME, &head, np))" 403.Pp 404Or, for simplicity, one can use the 405.Fn ARB_FOREACH 406or 407.Fn ARB_FOREACH_REVERSE 408macro: 409.Bd -ragged -offset indent 410.Fn RB_FOREACH np NAME head 411.Ed 412.Pp 413The macros 414.Fn ARB_FOREACH_SAFE 415and 416.Fn ARB_FOREACH_REVERSE_SAFE 417traverse the tree referenced by head 418in a forward or reverse direction respectively, 419assigning each element in turn to np. 420However, unlike their unsafe counterparts, 421they permit both the removal of np 422as well as freeing it from within the loop safely 423without interfering with the traversal. 424.Pp 425Both 426.Fn ARB_FOREACH_FROM 427and 428.Fn ARB_FOREACH_REVERSE_FROM 429may be used to continue an interrupted traversal 430in a forward or reverse direction respectively. 431The head pointer is not required. 432The pointer to the node from where to resume the traversal 433should be passed as their last argument, 434and will be overwritten to provide safe traversal. 435.Pp 436The 437.Fn ARB_EMPTY 438macro should be used to check whether a red-black tree is empty. 439.Pp 440Given that ARB trees have an intrinsic upper bound on the number of entries, 441some ARB-specific additional macros are defined. 442The 443.Fn ARB_FULL 444macro returns a boolean indicating whether the current number of tree entries 445equals the tree's maximum. 446The 447.Fn ARB_CURNODES 448and 449.Fn ARB_MAXNODES 450macros return the current and maximum number of entries respectively. 451The 452.Fn ARB_GETFREE 453macro returns a pointer to the next free entry in the array of entries, ready to 454be linked into the tree. 455The 456.Fn ARB_INSERT 457returns 458.Dv NULL 459if the element was inserted in the tree successfully, otherwise they 460return a pointer to the element with the colliding key. 461.Pp 462Accordingly, 463.Fn ARB_REMOVE 464returns the pointer to the removed element otherwise they return 465.Dv NULL 466to indicate an error. 467.Sh SEE ALSO 468.Xr queue 3 , 469.Xr tree 3 470.Sh HISTORY 471The 472.Nm ARB 473macros first appeared in 474.Fx 13.0 . 475.Sh AUTHORS 476The 477.Nm ARB 478macros were implemented by 479.An Lawrence Stewart Aq Mt lstewart@FreeBSD.org , 480based on 481.Xr tree 3 482macros written by 483.An Niels Provos . 484