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authorcvs2git <rtems-devel@rtems.org>2003-01-28 19:56:06 +0000
committercvs2git <rtems-devel@rtems.org>2003-01-28 19:56:06 +0000
commitabcd9035763ff87a4afd0b9adad5b77e4dbb52ec (patch)
tree7d52bf74324906a4adb23350ddea72f65b16ae90 /avl-1.4.0/avl.texinfo
parent66d25567fe424bb55fde088f3d45e9ed044400c1 (diff)
This commit was manufactured by cvs2svn to create tag 'rtems-addon-rtems-addon-packages-20030128
packages-20030128'. Sprout from ncurses-gnu 2002-12-19 15:34:54 UTC Eric Norum <WENorum@lbl.gov> 'Latest ncurses add-on' Cherrypick from addons 2002-06-28 21:58:41 UTC Eric Norum <WENorum@lbl.gov> 'Useful add-on libraries': README RTEMS_Makefiles/Makefile.avl RTEMS_Makefiles/Makefile.common RTEMS_Makefiles/Makefile.site avl-1.4.0/AUTHORS avl-1.4.0/COPYING avl-1.4.0/ChangeLog avl-1.4.0/INSTALL avl-1.4.0/Makefile.am avl-1.4.0/Makefile.in avl-1.4.0/NEWS avl-1.4.0/README avl-1.4.0/THANKS avl-1.4.0/TODO avl-1.4.0/aclocal.m4 avl-1.4.0/avl.c avl-1.4.0/avl.h avl-1.4.0/avl.html avl-1.4.0/avl.info avl-1.4.0/avl.texinfo avl-1.4.0/avl.text avl-1.4.0/avlt.c avl-1.4.0/avlt.h avl-1.4.0/avltr.c avl-1.4.0/avltr.h avl-1.4.0/configure avl-1.4.0/configure.in avl-1.4.0/install-sh avl-1.4.0/missing avl-1.4.0/mkinstalldirs avl-1.4.0/rb.c avl-1.4.0/rb.h avl-1.4.0/texinfo.tex avl-1.4.0/thread-test.c examples/avl/BuildTests.sh examples/avl/Makefile examples/avl/README examples/avl/init.c examples/ncurses/BuildTests.sh 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ncurses-5.2/ncurses/base/version.c ncurses-5.2/ncurses/base/vsscanf.c ncurses-5.2/ncurses/base/wresize.c ncurses-5.2/ncurses/curses.priv.h ncurses-5.2/ncurses/fifo_defs.h ncurses-5.2/ncurses/llib-lncurses ncurses-5.2/ncurses/modules ncurses-5.2/ncurses/tinfo/MKcaptab.awk ncurses-5.2/ncurses/tinfo/MKfallback.sh ncurses-5.2/ncurses/tinfo/MKnames.awk ncurses-5.2/ncurses/tinfo/README ncurses-5.2/ncurses/tinfo/access.c ncurses-5.2/ncurses/tinfo/add_tries.c ncurses-5.2/ncurses/tinfo/alloc_entry.c ncurses-5.2/ncurses/tinfo/alloc_ttype.c ncurses-5.2/ncurses/tinfo/captoinfo.c ncurses-5.2/ncurses/tinfo/comp_error.c ncurses-5.2/ncurses/tinfo/comp_expand.c ncurses-5.2/ncurses/tinfo/comp_hash.c ncurses-5.2/ncurses/tinfo/comp_parse.c ncurses-5.2/ncurses/tinfo/comp_scan.c ncurses-5.2/ncurses/tinfo/doalloc.c ncurses-5.2/ncurses/tinfo/free_ttype.c ncurses-5.2/ncurses/tinfo/getenv_num.c ncurses-5.2/ncurses/tinfo/home_terminfo.c ncurses-5.2/ncurses/tinfo/init_keytry.c ncurses-5.2/ncurses/tinfo/keys.list ncurses-5.2/ncurses/tinfo/lib_acs.c ncurses-5.2/ncurses/tinfo/lib_baudrate.c ncurses-5.2/ncurses/tinfo/lib_cur_term.c ncurses-5.2/ncurses/tinfo/lib_data.c ncurses-5.2/ncurses/tinfo/lib_has_cap.c ncurses-5.2/ncurses/tinfo/lib_kernel.c ncurses-5.2/ncurses/tinfo/lib_longname.c ncurses-5.2/ncurses/tinfo/lib_napms.c ncurses-5.2/ncurses/tinfo/lib_options.c ncurses-5.2/ncurses/tinfo/lib_print.c ncurses-5.2/ncurses/tinfo/lib_raw.c ncurses-5.2/ncurses/tinfo/lib_setup.c ncurses-5.2/ncurses/tinfo/lib_termcap.c ncurses-5.2/ncurses/tinfo/lib_termname.c ncurses-5.2/ncurses/tinfo/lib_tgoto.c ncurses-5.2/ncurses/tinfo/lib_ti.c ncurses-5.2/ncurses/tinfo/lib_tparm.c ncurses-5.2/ncurses/tinfo/lib_tputs.c ncurses-5.2/ncurses/tinfo/lib_ttyflags.c ncurses-5.2/ncurses/tinfo/make_keys.c ncurses-5.2/ncurses/tinfo/name_match.c ncurses-5.2/ncurses/tinfo/parse_entry.c ncurses-5.2/ncurses/tinfo/read_entry.c ncurses-5.2/ncurses/tinfo/read_termcap.c ncurses-5.2/ncurses/tinfo/setbuf.c ncurses-5.2/ncurses/tinfo/strings.c ncurses-5.2/ncurses/tinfo/write_entry.c ncurses-5.2/ncurses/trace/README ncurses-5.2/ncurses/trace/lib_trace.c ncurses-5.2/ncurses/trace/lib_traceatr.c ncurses-5.2/ncurses/trace/lib_tracebits.c ncurses-5.2/ncurses/trace/lib_tracechr.c ncurses-5.2/ncurses/trace/lib_tracedmp.c ncurses-5.2/ncurses/trace/lib_tracemse.c ncurses-5.2/ncurses/trace/trace_buf.c ncurses-5.2/ncurses/trace/trace_tries.c ncurses-5.2/ncurses/trace/trace_xnames.c ncurses-5.2/ncurses/tty/MKexpanded.sh ncurses-5.2/ncurses/tty/hardscroll.c ncurses-5.2/ncurses/tty/hashmap.c ncurses-5.2/ncurses/tty/lib_mvcur.c ncurses-5.2/ncurses/tty/lib_tstp.c ncurses-5.2/ncurses/tty/lib_twait.c ncurses-5.2/ncurses/tty/lib_vidattr.c ncurses-5.2/ncurses/tty/tty_display.h ncurses-5.2/ncurses/tty/tty_input.h ncurses-5.2/ncurses/tty/tty_update.c ncurses-5.2/panel/Makefile.in ncurses-5.2/panel/headers ncurses-5.2/panel/llib-lpanel ncurses-5.2/panel/modules ncurses-5.2/panel/p_above.c ncurses-5.2/panel/p_below.c ncurses-5.2/panel/p_bottom.c ncurses-5.2/panel/p_delete.c ncurses-5.2/panel/p_hidden.c ncurses-5.2/panel/p_hide.c ncurses-5.2/panel/p_move.c ncurses-5.2/panel/p_new.c ncurses-5.2/panel/p_replace.c ncurses-5.2/panel/p_show.c ncurses-5.2/panel/p_top.c ncurses-5.2/panel/p_update.c ncurses-5.2/panel/p_user.c ncurses-5.2/panel/p_win.c ncurses-5.2/panel/panel.c ncurses-5.2/panel/panel.h ncurses-5.2/panel/panel.priv.h ncurses-5.2/progs/MKtermsort.sh ncurses-5.2/progs/Makefile.in ncurses-5.2/progs/capconvert ncurses-5.2/progs/clear.c ncurses-5.2/progs/clear.sh ncurses-5.2/progs/dump_entry.c ncurses-5.2/progs/dump_entry.h ncurses-5.2/progs/infocmp.c ncurses-5.2/progs/modules ncurses-5.2/progs/progs.priv.h ncurses-5.2/progs/tic.c ncurses-5.2/progs/toe.c ncurses-5.2/progs/tput.c ncurses-5.2/progs/tset.c ncurses-5.2/sysdeps/unix/sysv/linux/Makefile ncurses-5.2/sysdeps/unix/sysv/linux/alpha/configure ncurses-5.2/sysdeps/unix/sysv/linux/configure ncurses-5.2/sysdeps/unix/sysv/linux/edit_man.sed ncurses-5.2/sysdeps/unix/sysv/linux/edit_man.sh ncurses-5.2/sysdeps/unix/sysv/linux/run_tic.sh ncurses-5.2/tack/COPYING ncurses-5.2/tack/HISTORY ncurses-5.2/tack/Makefile.in ncurses-5.2/tack/README ncurses-5.2/tack/ansi.c ncurses-5.2/tack/charset.c ncurses-5.2/tack/color.c ncurses-5.2/tack/control.c ncurses-5.2/tack/crum.c ncurses-5.2/tack/edit.c ncurses-5.2/tack/fun.c ncurses-5.2/tack/init.c ncurses-5.2/tack/menu.c ncurses-5.2/tack/modes.c ncurses-5.2/tack/modules ncurses-5.2/tack/output.c ncurses-5.2/tack/pad.c ncurses-5.2/tack/scan.c ncurses-5.2/tack/sync.c ncurses-5.2/tack/sysdep.c ncurses-5.2/tack/tack.1 ncurses-5.2/tack/tack.c ncurses-5.2/tack/tack.h ncurses-5.2/tar-copy.sh ncurses-5.2/test/Makefile.in ncurses-5.2/test/README ncurses-5.2/test/blue.c ncurses-5.2/test/bs.6 ncurses-5.2/test/bs.c ncurses-5.2/test/cardfile.c ncurses-5.2/test/cardfile.dat ncurses-5.2/test/configure ncurses-5.2/test/configure.in ncurses-5.2/test/ditto.c ncurses-5.2/test/dots.c ncurses-5.2/test/filter.c ncurses-5.2/test/firework.c ncurses-5.2/test/firstlast.c ncurses-5.2/test/gdc.6 ncurses-5.2/test/gdc.c ncurses-5.2/test/hanoi.c ncurses-5.2/test/hashtest.c ncurses-5.2/test/keynames.c ncurses-5.2/test/knight.c ncurses-5.2/test/lrtest.c ncurses-5.2/test/modules ncurses-5.2/test/ncurses.c ncurses-5.2/test/ncurses_tst.hin ncurses-5.2/test/newdemo.c ncurses-5.2/test/railroad.c ncurses-5.2/test/rain.c ncurses-5.2/test/tclock.c ncurses-5.2/test/test.priv.h ncurses-5.2/test/testaddch.c ncurses-5.2/test/testcurs.c ncurses-5.2/test/testscanw.c ncurses-5.2/test/tracemunch ncurses-5.2/test/view.c ncurses-5.2/test/worm.c ncurses-5.2/test/xmas.c Cherrypick from master 2003-01-28 19:56:05 UTC Joel Sherrill <joel.sherrill@OARcorp.com> '2003-01-28 Joel Sherrill <joel@OARcorp.com>': ChangeLog RTEMS_Makefiles/Makefile.bfd RTEMS_Makefiles/Makefile.libtecla RTEMS_Makefiles/Makefile.ncurses RTEMS_Makefiles/Makefile.ncurses-5.3 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libtecla-1.4.1/html/ef_expand_file.html libtecla-1.4.1/html/enhance.html libtecla-1.4.1/html/gl_get_line.html libtecla-1.4.1/html/index.html libtecla-1.4.1/html/libtecla.html libtecla-1.4.1/html/pca_lookup_file.html libtecla-1.4.1/html/release.html libtecla-1.4.1/install-sh libtecla-1.4.1/keytab.c libtecla-1.4.1/keytab.h libtecla-1.4.1/libtecla.h libtecla-1.4.1/libtecla.map libtecla-1.4.1/man3/cfc_file_start.3 libtecla-1.4.1/man3/cfc_literal_escapes.3 libtecla-1.4.1/man3/cfc_set_check_fn.3 libtecla-1.4.1/man3/cpl_add_completion.3 libtecla-1.4.1/man3/cpl_complete_word.3 libtecla-1.4.1/man3/cpl_file_completions.3 libtecla-1.4.1/man3/cpl_last_error.3 libtecla-1.4.1/man3/cpl_list_completions.3 libtecla-1.4.1/man3/cpl_record_error.3 libtecla-1.4.1/man3/del_CplFileConf.3 libtecla-1.4.1/man3/del_ExpandFile.3 libtecla-1.4.1/man3/del_GetLine.3 libtecla-1.4.1/man3/del_PathCache.3 libtecla-1.4.1/man3/del_PcaPathConf.3 libtecla-1.4.1/man3/del_WordCompletion.3 libtecla-1.4.1/man3/ef_expand_file.3 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+\input texinfo @c -*-texinfo-*-
+@c %**start of header
+@setfilename avl.info
+@settitle libavl manual
+@setchapternewpage on
+@c %**end of header
+
+@syncodeindex vr cp
+@syncodeindex fn cp
+@syncodeindex tp cp
+
+@ifinfo
+This file documents libavl, a library for the manipulation of balanced
+binary trees.
+
+Copyright 1998, 1999 Free Software Foundation, Inc.
+
+Permission is granted to make and distribute verbatim copies of this
+manual provided the copyright notice and this permission notice are
+preserved on all copies.
+
+@ignore
+Permission is granted to process this file through TeX and print the
+results, provided the printed document carries a copying permission
+notice identical to this one except for the removal of this paragraph
+(this paragraph not being relevant to the printed manual).
+
+@end ignore
+Permission is granted to copy and distribute modified versions of this
+manual under the conditions for verbatim copying, provided that the
+entire resulting derived work is distributed under the terms of a
+permission notice identical to this one.
+
+Permission is granted to copy and distribute translations of this manual
+into another language, under the above conditions for modified versions,
+except that this permission notice may be stated in a translation
+approved by the Free Software Foundation.
+@end ifinfo
+
+@titlepage
+@title libavl
+@subtitle A library for manipulation of balanced binary trees
+@author Ben Pfaff
+
+@page
+@vskip 0pt plus 1filll
+Copyright @copyright{} 1998, 1999 Free Software Foundation, Inc.
+
+Permission is granted to make and distribute verbatim copies of this
+manual provided the copyright notice and this permission notice are
+preserved on all copies.
+
+Permission is granted to copy and distribute modified versions of this
+manual under the conditions for verbatim copying, provided that the
+entire resulting derived work is distributed under the terms of a
+permission notice identical to this one.
+
+Permission is granted to copy and distribute translations of this manual
+into another language, under the above conditions for modified versions,
+except that this permission notice may be stated in a translation
+approved by the Free Software Foundation.
+@end titlepage
+
+@node Top, Introduction to balanced binary trees, (dir), (dir)
+
+@ifinfo
+This document describes libavl, a library for manipulation of balanced
+binary trees.
+
+This document applies to libavl version 1.4.0.
+@end ifinfo
+
+@menu
+* Introduction to balanced binary trees::
+* Introduction to threaded trees::
+* Types::
+* Functions::
+* Tree Creation::
+* Insertion::
+* Searching::
+* Iteration::
+* Conversion::
+* Author::
+* Index::
+@end menu
+
+@node Introduction to balanced binary trees, Introduction to threaded trees, Top, Top
+@chapter Introduction to balanced binary trees
+
+@cindex hash table
+Consider some techniques that can be used to find a particular item in a
+data set. Typical methods include sequential searching, digital
+searching, hash tables, and binary searching.
+
+Sequential searching is simple, but slow (O(n)). Digital searching
+requires that the entire data set be known in advance, and memory
+efficient implementations are slow.
+
+Hash tables are fast (O(1)) for static data sets, but they can be
+wasteful of memory. It can be difficult to choose an effective hash
+function. Some hash tables variants also make deletion an expensive
+operation.
+
+@cindex binary tree
+Binary search techniques work almost as quickly (O(log(n)) on an ordered
+table, or on a binary tree. Binary trees also allow easy iteration over
+the data in the tree in sorted order. With hash tables it is necessary
+to sort the data before iterating, and after sorting the data is no
+longer in hash form.
+
+Binary trees are efficient for insertion, deletion, and searching, if
+data are inserted in random order. But, if data are inserted in order
+using a naive algorithm, binary search degenerates to sequential search.
+
+@cindex red-black tree
+@cindex AVL tree
+@cindex rebalancing
+In turn, this problem can be solved by @dfn{rebalancing} the tree after
+each insertion or deletion. In rebalancing, nodes are rearranged via
+transformations called @dfn{rotations} using an algorithm that tends to
+minimize the tree's height.
+
+There are several schemes for rebalancing binary trees. The two most
+common types of balanced tree are @dfn{AVL trees} and @dfn{red-black
+trees}. libavl implements both types:
+
+@itemize @bullet
+@item
+@cindex Landis, E. M.
+@cindex Adel'son-Velskii, G. M.
+AVL trees, invented by Russian mathematicians G. M. Adel'son-Velskii and
+E. M. Landis, ensure that, for each node, the difference in height
+between its subtrees (the @dfn{balance factor}) is not greater than 1.
+
+@item
+Red-black trees, invented by R. Bayer and studied at length by
+L. J. Guibas and R. Sedgewick, assign each node of a tree a color (red
+or black), and specify a set of rules governing how red and black nodes
+may be arranged.
+@end itemize
+
+The table below presents a comparison among unbalanced binary trees, AVL
+trees, and red-black trees. In the table, @var{n} is the number of
+nodes in the tree and @var{h} is the tree's height before the
+operation. @dfn{lg} is the base-2 logarithm function.
+
+@multitable @columnfractions .05 .30 .35 .30
+
+@need 333
+@item @w{Operation}
+@item
+@tab Binary Tree
+@tab AVL Tree
+@tab Red-Black Tree
+
+@need 333
+@item @w{Time per insertion or deletion}
+@item
+@tab O(@var{h})
+@tab O(lg @var{n})
+@tab O(lg @var{n})
+
+@need 333
+@item @w{Time for insertion of @var{k} nodes having sequential values}
+@item
+@tab O(@math{@var{k}^2})
+@tab O(@var{n} lg @var{n})
+@tab O(@var{n} lg @var{n})
+
+@need 333
+@item @w{Time for insertion of @var{k} nodes having random values}
+@item
+@tab O(@var{n} lg @var{n})
+@tab O(@var{n} lg @var{n})
+@tab O(@var{n} lg @var{n})
+
+@need 333
+@item @w{Maximum number of rotations per insertion}
+@item
+@tab 0
+@tab 1
+@tab lg @var{n}
+
+@need 333
+@item @w{Maximum number of rotations per deletion}
+@item
+@tab 0
+@tab lg @var{n}
+@tab lg @var{n}
+
+@need 333
+@item @w{Maximum @var{h} as a function of @var{n}}
+@item
+@tab @var{n}
+@tab 1.44 lg (@var{n} + 2) - .328
+@tab 2 lg (@var{n} + 1)
+
+@need 333
+@item @w{Minimum @var{n} as a function of @var{h}}
+@item
+@tab @var{h}
+@tab 2^((@var{h} + .328) / 1.44) - 2
+@tab 2^(@var{h} / 2) - 1
+@end multitable
+
+There are alternatives to AVL trees that share some of their properties.
+For instance, skip lists, 2-3 trees, and splay trees all allow O(log(n))
+insertion and deletion. The main disadvantage of these methods is that
+their operations are not as well documented in the literature.
+
+@node Introduction to threaded trees, Types, Introduction to balanced binary trees, Top
+@chapter Introduction to threaded trees
+
+@dfn{Threading} is a clever method that simplifies binary tree
+traversal.
+
+Nodes in a unthreaded binary tree that have zero or one subnodes have
+two or one null subnode pointers, respectively. In a threaded binary
+tree, a left child pointer that would otherwise be null is used to point
+to the node's inorder@footnote{In tree traversal, @dfn{inorder} refers
+to visiting the nodes in their sorted order from smallest to largest.}
+predecessor, and in a null right child pointer points to its inorder
+successor.
+
+In a threaded tree, it is always possible to find the next node and the
+previous node of a node, given only a pointer to the node in question.
+In an unthreaded tree, it's also necessary to have a list of the nodes
+between the node in question and root of the tree.
+
+Advantages of a threaded tree compared to an unthreaded one include:
+
+@itemize @bullet
+@item
+Faster traversal and less memory usage during traversal, since no stack
+need be maintained.
+
+@item
+Greater generality, since one can go from a node to its successor or
+predecessor given only the node, simplifying algorithms that require
+moving forward and backward in a tree.
+@end itemize
+
+Some disadvantages of threaded trees are:
+
+@itemize @bullet
+@item
+Slower insertion and deletion, since threads need to be maintained. In
+somes cases, this can be alleviated by constructing the tree as an
+unthreaded tree, then threading it with a special libavl function.
+
+@item
+In theory, threaded trees need two extra bits per node to indicate
+whether each child pointer points to an ordinary node or the node's
+successor/predecessor node. In libavl, however, these bits are stored
+in a byte that is used for structure alignment padding in unthreaded
+binary trees, so no extra storage is used.
+@end itemize
+
+A @dfn{right-threaded binary tree} is similar to a threaded binary tree,
+but threads are only maintained on the right side of each node. This
+allows for traversal to the right (toward larger values) but not to the
+left (toward smaller values). Right-threaded trees are convenient when
+the properties of a threaded tree are desirable, but traversal in
+reverse sort order is not necessary. Not threading the left links saves
+time in insertions and deletions.
+
+Left-threaded binary trees also exist, but they are not implemented by
+libavl. The same effect can be obtained by sorting the tree in the
+opposite order.
+
+@node Types, Functions, Introduction to threaded trees, Top
+@chapter Types
+
+The following types are defined and used by libavl:
+
+@deftp {Data Type} avl_tree
+@deftpx {Data Type} avlt_tree
+@deftpx {Data Type} avltr_tree
+@deftpx {Data Type} rb_tree
+These are the data types used to represent a tree. Although they are
+defined in the libavl header files, it should never be necessary to
+access them directly. Instead, all accesses should take place through
+libavl functions.
+@end deftp
+
+@deftp {Data Type} avl_node
+@deftpx {Data Type} avlt_node
+@deftpx {Data Type} avltr_node
+@deftpx {Data Type} rb_node
+These are the data types used to represent individual nodes in a tree.
+Similar cautions apply as with @code{avl_tree} structures.
+@end deftp
+
+@deftp {Data Type} avl_traverser
+@deftpx {Data Type} avlt_traverser
+@deftpx {Data Type} avltr_traverser
+@deftpx {Data Type} rb_traverser
+These are the data types used by the @code{avl_traverse} family of
+functions to iterate across the tree. Again, these are opaque
+structures.
+@end deftp
+
+@deftp {Data Type} avl_comparison_func
+Every tree must have an ordering defined by a function of this type. It
+must have the following signature:
+
+@smallexample
+int @var{compare} (const void *@var{a}, const void *@var{b}, void *@var{param})
+@end smallexample
+
+The return value is expected to be like that returned by @code{strcmp}
+in the standard C library: negative if @var{a} < @var{b}, zero if
+@var{a} = @var{b}, positive if @var{a} > @var{b}. @var{param} is an
+arbitrary value defined by the user when the tree was created.
+@end deftp
+
+@deftp {Data Type} avl_node_func
+This is a class of function called to perform an operation on a data
+item. Functions of this type have the following signature:
+
+@smallexample
+void @var{operate} (void *@var{data}, void *@var{param})
+@end smallexample
+
+@var{data} is the data item and @var{param} is an arbitrary user-defined
+value set when the tree was created.
+@end deftp
+
+@deftp {Data Type} avl_copy_func
+
+This is a class of function called to make a new copy of a node's data.
+Functions of this type have the following signature:
+
+@smallexample
+void *@var{copy} (void *@var{data}, void *@var{param})
+@end smallexample
+
+The function should return a new copy of @var{data}. @var{param} is an
+arbitrary user-defined value set when the tree was created.
+@end deftp
+
+@defmac AVL_MAX_HEIGHT
+This macro defines the maximum height of an AVL tree that can be handled
+by functions that maintain a stack of nodes descended. The default
+value is 32, which allows for AVL trees with a maximum number of nodes
+between 5,704,880 and 4,294,967,295, depending on order of insertion.
+This macro may be defined by the user before including any AVL tree
+header file, in which case libavl will honor that value.
+@end defmac
+
+@defmac RB_MAX_HEIGHT
+This macro defines the maximum height of an AVL tree that can be handled
+by functions that maintain a stack of nodes descended. The default
+value is 32, which allows for red-black trees with a maximum number of
+nodes of at least 65535. This macro may be defined by the user before
+including the red-black tree header file, in which case libavl will
+honor that value.
+@end defmac
+
+@node Functions, Tree Creation, Types, Top
+@chapter Functions
+
+@cindex unthreaded
+@cindex threads
+@cindex right threads
+libavl is four libraries in one:
+
+@itemize @bullet
+@item
+An unthreaded AVL tree library.
+
+@item
+A threaded AVL tree library.
+
+@item
+A right-threaded AVL tree library.
+
+@item
+A red-black tree library.
+@end itemize
+
+Identifiers in these libraries are prefixed by @code{avl_},
+@code{avlt_}, @code{avltr_}, and @code{rb_}, with corresponding header
+files @file{avl.h}, @file{avlt.h}, @file{avltr.h}, and @file{rb.h},
+respectively. The functions that they declare are defined in the
+@file{.c} files with the same names.
+
+Most tree functions are implemented in all three libraries, but
+threading allows more generality of operation. So, the threaded and
+right-threaded libraries offer a few additional functions for finding
+the next or previous node from a given node. In addition, they offer
+functions for converting trees from threaded or right-threaded
+representations to unthreaded, and vice versa.@footnote{In general, you
+should build the sort of tree that you need to use, but occasionally it
+is useful to convert between tree types.}
+
+@node Tree Creation, Insertion, Functions, Top
+@chapter Tree Creation
+
+These functions deal with creation and destruction of AVL trees.
+
+@deftypefun {avl_tree *} avl_create (avl_comparison_func @var{compare}, void *@var{param})
+@deftypefunx {avlt_tree *} avlt_create (avlt_comparison_func @var{compare}, void *@var{param})
+@deftypefunx {avltr_tree *} avltr_create (avltr_comparison_func @var{compare}, void *@var{param})
+@deftypefunx {rb_tree *} rb_create (avl_comparison_func @var{compare}, void *@var{param})
+Create a new, empty tree with comparison function @var{compare}.
+Arbitrary user data @var{param} is saved so that it can be passed to
+user callback functions.
+@end deftypefun
+
+@deftypefun {void} avl_destroy (avl_tree *@var{tree}, avl_node_func @var{free})
+@deftypefunx {void} avlt_destroy (avlt_tree *@var{tree}, avl_node_func @var{free})
+@deftypefunx {void} avltr_destroy (avltr_tree *@var{tree}, avl_node_func @var{free})
+@deftypefunx {void} rb_destroy (rb_tree *@var{tree}, avl_node_func @var{free})
+Destroys @var{tree}, releasing all of its storage. If @var{free} is
+non-null, then it is called for every node in postorder before that node
+is freed.
+@end deftypefun
+
+@deftypefun {void} avl_free (avl_tree *@var{tree})
+@deftypefunx {void} avlt_free (avlt_tree *@var{tree})
+@deftypefunx {void} avltr_free (avltr_tree *@var{tree})
+@deftypefunx {void} rb_free (rb_tree *@var{tree})
+Destroys @var{tree}, releasing all of its storage. The data in each
+node is freed with a call to the standard C library function
+@code{free}.
+@end deftypefun
+
+@deftypefun {avl_tree *} avl_copy (const avl_tree *@var{tree}, avl_copy_func @var{copy})
+@deftypefunx {avlt_tree *} avl_copy (const avlt_tree *@var{tree}, avl_copy_func @var{copy})
+@deftypefunx {avltr_tree *} avl_copy (const avltr_tree *@var{tree}, avl_copy_func @var{copy})
+@deftypefunx {rb_tree *} rb_copy (const rb_tree *@var{tree}, avl_copy_func @var{copy})
+Copies the contents of @var{tree} into a new tree, and returns the new
+tree. If @var{copy} is non-null, then it is called to make a new copy
+of each node's data; otherwise, the node data is copied verbatim into
+the new tree.
+@end deftypefun
+
+@deftypefun int avl_count (const avl_tree *@var{tree})
+@deftypefunx int avlt_count (const avlt_tree *@var{tree})
+@deftypefunx int avltr_count (const avltr_tree *@var{tree})
+@deftypefunx int rb_count (const rb_tree *@var{tree})
+Returns the number of nodes in @var{tree}.
+@end deftypefun
+
+@deftypefun {void *} xmalloc (size_t @var{size})
+This is not a function defined by libavl. Instead, it is a function
+that the user program can define. It must allocate @var{size} bytes
+using @code{malloc} and return it. It can handle out-of-memory errors
+however it chooses, but it may not ever return a null pointer.
+
+If there is an @code{xmalloc} function defined for use by libavl, the
+source files (@file{avl.c}, @file{avlt.c}, @file{avltr.c}, @file{rb.c})
+must be compiled with @code{HAVE_XMALLOC} defined. Otherwise, the
+library will use its internal static @code{xmalloc}, which handles
+out-of-memory errors by printing a message @samp{virtual memory
+exhausted} to stderr and terminating the program with exit code
+@code{EXIT_FAILURE}.
+@end deftypefun
+
+@node Insertion, Searching, Tree Creation, Top
+@chapter Insertion and Deletion
+
+These function insert nodes, delete nodes, and search for nodes in
+trees.
+
+@deftypefun {void **} avl_probe (avl_tree *@var{tree}, void *@var{data})
+@deftypefunx {void **} avlt_probe (avlt_tree *@var{tree}, void *@var{data})
+@deftypefunx {void **} avltr_probe (avltr_tree *@var{tree}, void *@var{data})
+@deftypefunx {void **} rb_probe (rb_tree *@var{tree}, void *@var{data})
+These are the workhorse functions for tree insertion. They search
+@var{tree} for a node with data matching @var{data}. If found, a
+pointer to the matching data is returned. Otherwise, a new node is
+created for @var{data}, and a pointer to that data is returned. In
+either case, the pointer returned can be changed by the user, but the
+key data used by the tree's comparison must not be changed@footnote{It
+can be changed if this would not change the ordering of the nodes in the
+tree; i.e., if this would not cause the data in the node to be less than
+or equal to the previous node's data or greater than or equal to the
+next node's data.}.
+
+It is usually easier to use one of the @code{avl_insert} or
+@code{avl_replace} functions instead of @code{avl_probe} directly.
+
+@strong{Please note:} It's not a particularly good idea to insert a null
+pointer as a data item into a tree, because several libavl functions
+return a null pointer to indicate failure. You can sometimes avoid a
+problem by using functions that return a pointer to a pointer instead of
+a plain pointer. Also be wary of this when casting an arithmetic type
+to a void pointer for insertion---on typical architectures, 0's become
+null pointers when this is done.
+@end deftypefun
+
+@deftypefun {void *} avl_insert (avl_tree *@var{tree}, void *@var{data})
+@deftypefunx {void *} avlt_insert (avlt_tree *@var{tree}, void *@var{data})
+@deftypefunx {void *} avltr_insert (avltr_tree *@var{tree}, void *@var{data})
+@deftypefunx {void *} rb_insert (rb_tree *@var{tree}, void *@var{data})
+If a node with data matching @var{data} exists in @var{tree}, returns
+the matching data item. Otherwise, inserts @var{data} into @var{tree}
+and returns a null pointer.
+@end deftypefun
+
+@deftypefun void avl_force_insert (avl_tree *@var{tree}, void *@var{data})
+@deftypefunx void avlt_force_insert (avlt_tree *@var{tree}, void *@var{data})
+@deftypefunx void avltr_force_insert (avltr_tree *@var{tree}, void *@var{data})
+@deftypefunx void rb_force_insert (rb_tree *@var{tree}, void *@var{data})
+Inserts @var{data} into @var{tree}. If a node with data matching
+@var{data} exists in @var{tree}, aborts the program with an assertion
+violation. This function is implemented as a macro; if it is used, the
+standard C header @code{assert.h} must also be included. If macro
+@code{NDEBUG} is defined when a libavl header is included, these
+functions are short-circuited to a direct call to @code{avl_insert},
+and no check is performed.
+@end deftypefun
+
+@deftypefun {void *} avl_replace (avl_tree *@var{tree}, void *@var{data})
+@deftypefunx {void *} avlt_replace (avlt_tree *@var{tree}, void *@var{data})
+@deftypefunx {void *} avltr_replace (avltr_tree *@var{tree}, void *@var{data})
+@deftypefunx {void *} rb_replace (rb_tree *@var{tree}, void *@var{data})
+If a node with data matching @var{data}, such that the comparison
+function returns 0, exists in @var{tree}, replaces the node's data with
+@var{data} and returns the node's former contents. Otherwise, inserts
+@var{data} into @var{tree} and returns a null pointer.
+@end deftypefun
+
+@deftypefun {void *} avl_delete (avl_tree *@var{tree}, const void *@var{data})
+@deftypefunx {void *} avlt_delete (avlt_tree *@var{tree}, const void *@var{data})
+@deftypefunx {void *} avltr_delete (avltr_tree *@var{tree}, const void *@var{data})
+@deftypefunx {void *} rb_delete (rb_tree *@var{tree}, const void *@var{data})
+Searches @var{tree} for a node with data matching @var{data}. If found,
+the node is deleted and its data is returned. Otherwise, returns a null
+pointer.
+@end deftypefun
+
+@deftypefun {void *} avl_force_delete (avl_tree *@var{tree}, const void *@var{data})
+@deftypefunx {void *} avlt_force_delete (avlt_tree *@var{tree}, const void *@var{data})
+@deftypefunx {void *} avltr_force_delete (avltr_tree *@var{tree}, const void *@var{data})
+@deftypefunx {void *} rb_force_delete (rb_tree *@var{tree}, const void *@var{data})
+Deletes a node with data matching @var{data} from @var{tree}. If no
+matching node is found, aborts the program with an assertion violation.
+If macro @code{NDEBUG} is declared when a libavl header is included,
+these functions are short-circuited to a direct call to
+@code{avl_delete}, and no check is performed.
+@end deftypefun
+
+@node Searching, Iteration, Insertion, Top
+@chapter Searching
+
+These function search a tree for an item without making an insertion or
+a deletion.
+
+@deftypefun {void *} avl_find (avl_tree *@var{tree}, const void *@var{data})
+@deftypefunx {void **} avlt_find (avlt_tree *@var{tree}, const void *@var{data})
+@deftypefunx {void **} avltr_find (avltr_tree *@var{tree}, const void *@var{data})
+@deftypefunx {void *} rb_find (rb_tree *@var{tree}, const void *@var{data})
+Searches @var{tree} for a node with data matching @var{data}, If found,
+returns the node's data (for threaded and right-threaded trees, a
+pointer to the node's data). Otherwise, returns a null pointer.
+@end deftypefun
+
+@deftypefun {void *} avl_find_close (avl_tree *@var{tree}, const void *@var{data})
+@deftypefunx {void **} avlt_find_close (avlt_tree *@var{tree}, const void *@var{data})
+@deftypefunx {void **} avltr_find_close (avltr_tree *@var{tree}, const void *@var{data})
+@deftypefunx {void *} rb_find_close (rb_tree *@var{tree}, const void *@var{data})
+Searches @var{tree} for a node with data matching @var{data}. If found,
+returns the node's data (for threaded and right-threaded trees, a
+pointer to the node's data). If no matching item is found, then it
+finds a node whose data is ``close'' to @var{data}; either the node
+closest in value to @var{data}, or the node either before or after the
+node with the closest value. Returns a null pointer if the tree does
+not contain any nodes.
+@end deftypefun
+
+@node Iteration, Conversion, Searching, Top
+@chapter Iteration
+
+These functions allow the caller to iterate across the items in a tree.
+
+@deftypefun void avl_walk (const avl_tree *@var{tree}, avl_node_func @var{operate}, void *@var{param})
+@deftypefunx void avlt_walk (const avlt_tree *@var{tree}, avl_node_func @var{operate}, void *@var{param})
+@deftypefunx void avltr_walk (const avltr_tree *@var{tree}, avl_node_func @var{operate}, void *@var{param})
+@deftypefunx void rb_walk (const rb_tree *@var{tree}, avl_node_func @var{operate}, void *@var{param})
+Walks through all the nodes in @var{tree}, and calls function
+@var{operate} for each node in inorder. @var{param} overrides the value
+passed to @code{avl_create} (and family) for this operation only.
+@var{operate} must not change the key data in the nodes in a way that
+would reorder the data values or cause two values to become equal.
+@end deftypefun
+
+@deftypefun {void *} avl_traverse (const avl_tree *@var{tree}, avl_traverser *@var{trav})
+@deftypefunx {void *} avlt_traverse (const avlt_tree *@var{tree}, avlt_traverser *@var{trav})
+@deftypefunx {void *} avltr_traverse (const avltr_tree *@var{tree}, avltr_traverser *@var{trav})
+@deftypefunx {void *} rb_traverse (const rb_tree *@var{tree}, rb_traverser *@var{trav})
+Returns each of @var{tree}'s nodes' data values in sequence, then a null
+pointer to indicate the last item. @var{trav} must be initialized
+before the first call, either in a declaration like that below, or using
+one of the functions below.
+
+@smallexample
+avl_traverser trav = AVL_TRAVERSER_INIT;
+@end smallexample
+
+Each @code{avl_traverser} (and family) is a separate, independent
+iterator.
+
+For threaded and right-threaded trees, @code{avlt_next} or
+@code{avltr_next}, respectively, are faster and more memory-efficient
+than @code{avlt_traverse} or @code{avltr_traverse}.
+@end deftypefun
+
+@deftypefun {void *} avl_init_traverser (avl_traverser *@var{trav})
+@deftypefunx {void *} avlt_init_traverser (avlt_traverser *@var{trav})
+@deftypefunx {void *} avltr_init_traverser (avltr_traverser *@var{trav})
+@deftypefunx {void *} rb_init_traverser (rb_traverser *@var{trav})
+Initializes the specified tree traverser structure. After this function
+is called, the next call to the corresponding @code{*_traverse} function
+will return the smallest value in the appropriate tree.
+@end deftypefun
+
+@deftypefun {void **} avlt_next (const avlt_tree *@var{tree}, void **@var{data})
+@deftypefunx {void **} avltr_next (const avltr_tree *@var{tree}, void **@var{data})
+@var{data} must be a null pointer or a pointer to a data item in AVL
+tree @var{tree}. Returns a pointer to the next data item after
+@var{data} in @var{tree} in inorder (this is the first item if
+@var{data} is a null pointer), or a null pointer if @var{data} was the
+last item in @var{tree}.
+@end deftypefun
+
+@deftypefun {void **} avltr_prev (const avltr_tree *@var{tree}, void **@var{data})
+@var{data} must be a null pointer or a pointer to a data item in AVL
+tree @var{tree}. Returns a pointer to the previous data item before
+@var{data} in @var{tree} in inorder (this is the last, or greatest
+valued, item if @var{data} is a null pointer), or a null pointer if
+@var{data} was the first item in @var{tree}.
+@end deftypefun
+
+@node Conversion, Author, Iteration, Top
+@chapter Conversion
+
+@deftypefun {avlt_tree *} avlt_thread (avl_tree *@var{tree})
+@deftypefunx {avltr_tree *} avltr_thread (avl_tree *@var{tree})
+Adds symmetric threads or right threads, respectively, to unthreaded AVL
+tree @var{tree} and returns a pointer to @var{tree} cast to the
+appropriate type. After one of these functions is called, threaded or
+right-threaded functions, as appropriate, must be used with @var{tree};
+unthreaded functions may not be used.
+@end deftypefun
+
+@deftypefun {avl_tree *} avlt_unthread (avlt_tree *@var{tree})
+@deftypefunx {avl_tree *} avltr_unthread (avltr_tree *@var{tree})
+Cuts all threads in threaded or right-threaded, respectively, AVL tree
+@var{tree} and returns a pointer to @var{tree} cast to @code{avl_tree
+*}. After one of these functions is called, unthreaded functions must
+be used with @var{tree}; threaded or right-threaded functions may not be
+used.
+@end deftypefun
+
+@node Author, Index, Conversion, Top
+@chapter Author
+
+@cindex Pfaff, Benjamin Levy
+@cindex author
+@cindex Knuth, Donald Ervin
+@cindex @cite{Art of Computer Programming}
+libavl was written by Ben Pfaff @email{blp@@gnu.org}.
+
+libavl's generic tree algorithms and AVL algorithms are based on those
+found in Donald Knuth's venerable @cite{Art of Computer Programming}
+series from Addison-Wesley, primarily Volumes 1 and 3. libavl's
+red-black tree algorithms are based on those found in Cormen et al.,
+@cite{Introduction to Algorithms}, 2nd ed., from MIT Press.
+
+@node Index, , Author, Top
+@unnumbered Index
+
+@printindex cp
+
+@contents
+@bye