@node Container data types
@section Container data types

@c Copyright (C) 2019--2021 Free Software Foundation, Inc.

@c Permission is granted to copy, distribute and/or modify this document
@c under the terms of the GNU Free Documentation License, Version 1.3 or
@c any later version published by the Free Software Foundation; with no
@c Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.  A
@c copy of the license is at <https://www.gnu.org/licenses/fdl-1.3.en.html>.

@c Written by Bruno Haible.

@c This macro expands to \log in TeX mode, but just 'log' in HTML and info
@c modes.
@ifnottex
@macro log
log
@end macro
@end ifnottex

@c This macro expands to \mathopsup in TeX mode, to a superscript in HTML
@c mode, and to ^ without braces in info mode.
@ifhtml
@macro mathopsup {EXP}
@sup{\EXP\}
@end macro
@end ifhtml
@ifinfo
@macro mathopsup {EXP}
^\EXP\
@end macro
@end ifinfo

Gnulib provides several generic container data types.  They can be used
to organize collections of application-defined objects.

@node Ordinary containers
@subsection Ordinary container data types

@multitable @columnfractions .15 .5 .1 .1 .15
@headitem Data type
@tab Details
@tab Module
@tab Main include file
@tab Include file for operations with out-of-memory checking
@item Sequential list
@tab Can contain any number of objects in any given order.
     Duplicates are allowed, but can optionally be forbidden.
@tab @code{list}
@tab @code{"gl_list.h"}
@tab @code{"gl_xlist.h"}
@item Set
@tab Can contain any number of objects; the order does not matter.
     Duplicates (in the sense of the comparator) are forbidden.
@tab @code{set}
@tab @code{"gl_set.h"}
@tab @code{"gl_xset.h"}
@item Ordered set
@tab Can contain any number of objects in the order of a given comparator
     function.
     Duplicates (in the sense of the comparator) are forbidden.
@tab @code{oset}
@tab @code{"gl_oset.h"}
@tab @code{"gl_xoset.h"}
@item Map
@tab Can contain any number of (key, value) pairs, where keys and values
     are objects;
     there are no (key, value1) and (key, value2) pairs with the same key
     (in the sense of a given comparator function).
@tab @code{map}
@tab @code{"gl_map.h"}
@tab @code{"gl_xmap.h"}
@item Ordered map
@tab Can contain any number of (key, value) pairs, where keys and values
     are objects;
     the (key, value) pairs are ordered by the key, in the order of a given
     comparator function;
     there are no (key, value1) and (key, value2) pairs with the same key
     (in the sense of the comparator function).
@tab @code{omap}
@tab @code{"gl_omap.h"}
@tab @code{"gl_xomap.h"}
@end multitable

Operations without out-of-memory checking (suitable for use in libraries) are
declared in the ``main include file''.  Whereas operations with out-of-memory
checking (suitable only in programs) are declared in the ``include file for
operations with out-of-memory checking''.

For each of the data types, several implementations are available, with
different performance profiles with respect to the available operations.
This enables you to start with the simplest implementation (ARRAY) initially,
and switch to a more suitable implementation after profiling your application.
The implementation of each container instance is specified in a single place
only: in the invocation of the function @code{gl_*_create_empty} that creates
the instance.

The implementations and the guaranteed average performance for the operations
for the ``sequential list'' data type are:

@multitable @columnfractions 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
@headitem Operation
@tab ARRAY
@tab CARRAY
@tab LINKED
@tab TREE
@tab LINKEDHASH with duplicates
@tab LINKEDHASH without duplicates
@tab TREEHASH with duplicates
@tab TREEHASH without duplicates
@item @code{gl_list_size}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@item @code{gl_list_node_value}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@item @code{gl_list_node_set_value}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(1)}
@item @code{gl_list_next_node}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_list_previous_node}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_list_first_node}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_list_last_node}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_list_get_at}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_list_get_first}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_list_get_last}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_list_set_at}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_set_first}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_set_last}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_search}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@item @code{gl_list_search_from}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_search_from_to}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_indexof}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_list_indexof_from}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_indexof_from_to}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_add_first}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_add_last}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_add_before}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_add_after}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_add_at}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_remove_node}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_remove_at}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_remove_first}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_remove_last}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_remove}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(1)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_list_iterator}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_list_iterator_from_to}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_list_iterator_next}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(1)}
@tab @math{O(1)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_sortedlist_search}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_sortedlist_search_from}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_sortedlist_indexof}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_sortedlist_indexof_from}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_sortedlist_add}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@item @code{gl_sortedlist_remove}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O(@log n)}
@tab @math{O(n)}
@tab @math{O(n)}
@tab @math{O((@log n)@mathopsup{2})}
@tab @math{O(@log n)}
@end multitable

The implementations and the guaranteed average performance for the operations
for the ``set'' data type are:

@multitable @columnfractions 0.4 0.2 0.4
@headitem Operation
@tab ARRAY
@tab LINKEDHASH, HASH
@item @code{gl_set_size}
@tab @math{O(1)}
@tab @math{O(1)}
@item @code{gl_set_add}
@tab @math{O(n)}
@tab @math{O(1)}
@item @code{gl_set_remove}
@tab @math{O(n)}
@tab @math{O(1)}
@item @code{gl_set_search}
@tab @math{O(n)}
@tab @math{O(1)}
@item @code{gl_set_iterator}
@tab @math{O(1)}
@tab @math{O(1)}
@item @code{gl_set_iterator_next}
@tab @math{O(1)}
@tab @math{O(1)}
@end multitable

The implementations and the guaranteed average performance for the operations
for the ``ordered set'' data type are:

@multitable @columnfractions 0.5 0.25 0.25
@headitem Operation
@tab ARRAY
@tab TREE
@item @code{gl_oset_size}
@tab @math{O(1)}
@tab @math{O(1)}
@item @code{gl_oset_add}
@tab @math{O(n)}
@tab @math{O(@log n)}
@item @code{gl_oset_remove}
@tab @math{O(n)}
@tab @math{O(@log n)}
@item @code{gl_oset_search}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_oset_search_atleast}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_oset_iterator}
@tab @math{O(1)}
@tab @math{O(@log n)}
@item @code{gl_oset_iterator_next}
@tab @math{O(1)}
@tab @math{O(@log n)}
@end multitable

The implementations and the guaranteed average performance for the operations
for the ``map'' data type are:

@multitable @columnfractions 0.4 0.2 0.4
@headitem Operation
@tab ARRAY
@tab LINKEDHASH, HASH
@item @code{gl_map_size}
@tab @math{O(1)}
@tab @math{O(1)}
@item @code{gl_map_get}
@tab @math{O(n)}
@tab @math{O(1)}
@item @code{gl_map_put}
@tab @math{O(n)}
@tab @math{O(1)}
@item @code{gl_map_remove}
@tab @math{O(n)}
@tab @math{O(1)}
@item @code{gl_map_search}
@tab @math{O(n)}
@tab @math{O(1)}
@item @code{gl_map_iterator}
@tab @math{O(1)}
@tab @math{O(1)}
@item @code{gl_map_iterator_next}
@tab @math{O(1)}
@tab @math{O(1)}
@end multitable

The implementations and the guaranteed average performance for the operations
for the ``ordered map'' data type are:

@multitable @columnfractions 0.5 0.25 0.25
@headitem Operation
@tab ARRAY
@tab TREE
@item @code{gl_omap_size}
@tab @math{O(1)}
@tab @math{O(1)}
@item @code{gl_omap_get}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_omap_put}
@tab @math{O(n)}
@tab @math{O(@log n)}
@item @code{gl_omap_remove}
@tab @math{O(n)}
@tab @math{O(@log n)}
@item @code{gl_omap_search}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_omap_search_atleast}
@tab @math{O(@log n)}
@tab @math{O(@log n)}
@item @code{gl_omap_iterator}
@tab @math{O(1)}
@tab @math{O(@log n)}
@item @code{gl_omap_iterator_next}
@tab @math{O(1)}
@tab @math{O(@log n)}
@end multitable

For C++, Gnulib provides a C++ template class for each of these container data types.

@multitable @columnfractions .30 .20 .25 .25
@headitem Data type
@tab C++ class
@tab Module
@tab Include file
@item Sequential list
@tab @code{gl_List}
@tab @code{list-c++}
@tab @code{"gl_list.hh"}
@item Set
@tab @code{gl_Set}
@tab @code{set-c++}
@tab @code{"gl_set.hh"}
@item Ordered set
@tab @code{gl_OSet}
@tab @code{oset-c++}
@tab @code{"gl_oset.hh"}
@item Map
@tab @code{gl_Map}
@tab @code{map-c++}
@tab @code{"gl_map.hh"}
@item Ordered map
@tab @code{gl_OMap}
@tab @code{omap-c++}
@tab @code{"gl_omap.hh"}
@end multitable

@node Specialized containers
@subsection Specialized container data types

The @code{hamt} module implements the hash array mapped trie (HAMT) data
structure.  This is a data structure that contains (key, value) pairs.
Lookup of a (key, value) pair given the key is on average an @math{O(1)}
operation, assuming a good hash function for the keys is employed.

The HAMT data structure is useful when you want modifications (additions
of pairs, removal, value changes) to be visible only to some part of
your program, whereas other parts of the program continue to use the
unmodified HAMT.  The HAMT makes this possible in a space-efficient
manner: the modified and the unmodified HAMT share most of their
allocated memory.  It is also time-efficient: Every such modification
is @math{O(1)} on average, again assuming a good hash function for the keys.

A HAMT can be used whenever an ordinary hash table would be used.  It
does however, provide non-destructive updating operations without the
need to copy the whole container. On the other hand, a hash table is
simpler so that its performance may be better when non-destructive
update operations are not needed.

For example, a HAMT can be used to model the dynamic environment in a
LISP interpreter.  Updating a value in the dynamic environment of one
continuation frame would not modify values in earlier frames.

To use the module, include @code{hamt.h} in your code.  The public
interface is documented in that header file.  You have to provide a hash
function and an equivalence relation, which defines key equality.  The
module includes a test file @code{test-hamt.c}, which demonstrates how
the API can be used.

In the current implementation, each inner node of the HAMT can store up
to @math{32 = 2^5} entries and subtries.  Whenever a collision between
the initial bits of the hash values of two entries would happen, the
next @math{5} bits of the hash values are examined and the two entries
pushed down one level in the trie.

HAMTs have the same average access times as hash tables but grow and
shrink dynamically, so they use memory more economically and do not have
to be periodically resized.

They were described and analyzed in @cite{Phil Bagwell (2000). Ideal
Hash Trees (Report). Infoscience Department, École Polytechnique
Fédérale de Lausanne.}

The persistence aspect of the HAMT data structure, which means that each
updating operation (like inserting, replacing, or removing an entry)
returns a new HAMT while leaving the original one intact, is achieved
through structure sharing, which is even safe in the presence of
multiple threads when the used C compiler supports atomics.

@ifnottex
@unmacro log
@end ifnottex
@ifhtml
@unmacro mathopsup
@end ifhtml
@ifinfo
@unmacro mathopsup
@end ifinfo
