\input texinfo  @c -*-texinfo-*-

@settitle User's Guide to the GNU C++ Class Library
@setfilename libg++.info

@ifinfo
@format
START-INFO-DIR-ENTRY
* Libg++::                      The g++ class library.
END-INFO-DIR-ENTRY
@end format
@end ifinfo

@ifinfo
This file documents the features and implementation of The GNU C++ library

Copyright (C) 1988, 1991, 1992 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 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 also that the
section entitled ``GNU Library General Public License'' is included exactly as
in the original, and 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 the section entitled ``GNU Library General Public License'' and
this permission notice may be included in translations approved by the
Free Software Foundation instead of in the original English.
@end ifinfo

@iftex
@finalout
@c @smallbook
@c @cropmarks
@end iftex

@setchapternewpage odd

@titlepage
@title User's Guide
@title to the GNU C++ Library
@sp 3
@subtitle last updated April 29, 1992
@subtitle for version 2.0
@author Doug Lea (dl@@g.oswego.edu)
@page
@vskip 0pt plus 1filll
Copyright @copyright{} 1988, 1991, 1992 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 also that the
section entitled ``GNU Library General Public License'' is included exactly as
in the original, and 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 the section entitled ``GNU Library General Public License'' may be
included in a translation approved by the author instead of in the original
English.

@strong{Note: The GNU C++ library is still in test release. You will
be performing a valuable service if you report any bugs you encounter.}

@end titlepage

@ifinfo
@node Top, Copying, , (DIR)

Introduction
************

This manual documents how to install and use the GNU C++ library.

@end ifinfo
@menu
* Copying::	    GNU Library Public License says how you can copy
                    and share the GNU C++ library.
* Contributors::    People who have contributed to GNU C++ library.
* Installation::    How to configure, compile and install GNU C++ library
* Trouble::         If you have trouble installing GNU C++ library.
* General::         Aims, objectives, and limitations of the GNU C++ library
* Conventions::     Stylistic conventions
* OK::              Support for representation invariants
* Proto::           Introduction to container class prototypes
* Pix::             Pseudo-indexes
* Representations:: How variable-sized objects are represented
* Expressions::     Some guidance on programming expression-oriented classes
* Headers::         Header files and other support for interfacing C++ to C
* Builtin::         Utility functions for builtin types
* New::             Library dynamic allocation primitives
* IOStream:(iostream)Top.
                    The input/output library (istreams and ostreams).
* Stream::          obsolete I/O library
* Obstack::         Obstacks and their uses.
* AllocRing::       A place to store objects for a while
* String::          String, SubString, and Regex classes.
* Integer::         Multiple precision Integer class.
* Rational::        Multiple precision Rational class
* Complex::         Complex number class
* Fix::             Fixed point proportion classes
* Bit::             BitSet and BitString classes
* Random::          Random number generators
* Data::            SampleStatistic and related classes for data collection
* Curses::          CursesWindow class
* List::            Lisp-like List prototype
* LinkList::        Singly and doubly linked list class prototypes
* Vector::          Vector prototypes
* Plex::            Plex (adjustable array) prototypes
* Stack::           Stack prototypes
* Queue::           Queue prototypes
* Deque::           Double ended queue prototypes
* PQ::              Heap (priority queue) class prototypes
* Set::             Set class prototypes
* Bag::             Bag class prototypes
* Map::             Map (Associative array) prototypes
* GetOpt::          C++ class-based version of the GNU/UNIX getopt function
* Projects::	    Things Still Left to do
@end menu

@node Copying, Contributors, Top, Top
@include lgpl.texinfo

@node Contributors, Installation, Copying, Top
@unnumbered Contributors to GNU C++ library

Aside from Michael Tiemann, who worked out the front end for GNU C++, and
Richard Stallman, who worked out the back end, the following people (not
including those who have made their contributions to GNU CC) should not go
unmentioned.

@itemize @bullet
@item
Doug Lea contributed most otherwise unattributed classes.

@item
Per Bothner contributed the iostream I/O classes.

@item 
Dirk Grunwald contributed the Random number generation classes,
and PairingHeaps.

@item 
Kurt Baudendistel contributed Fixed precision reals.

@item 
Doug Schmidt contributed ordered hash tables, a perfect
hash function generator, and several other utilities.

@item
Marc Shapiro contributed the ideas and preliminary code for Plexes.

@item
Eric Newton contributed the curses window classes.

@item
Some of the I/O code is derived from BSD 4.4,
and was developed by the University of California, Berkeley.

@item
The code for converting accurately between floating point numbers
and their string representations was written by David M. Gay of AT&T.
@end itemize

@node Installation, Trouble, Contributors, Top
@chapter Installing GNU C++ library


@enumerate
@item
Read through the README file and the Makefile. Make sure that all
paths, system-dependent compile switches, and program names are correct.

@item
Check that files  @file{values.h}, @file{stdio.h},
and @file{math.h} declare and define values appropriate for your
system.

@item
Type @samp{make all} to compile the library, test, and install.
Current details about contents of the tests and utilities are in the 
@file{README} file.

@end enumerate

@node Trouble, General, Installation, Top
@chapter Trouble in Installation

Here are some of the things that have caused trouble for people installing
GNU C++ library.

@enumerate
@item
Make sure that your GNU C++ version number is at least as high as your
libg++ version number. For example, libg++ 1.22.0 requires g++ 1.22.0 or
later releases.

@item
Double-check system constants in the header files mentioned above.

@end enumerate

@node General, Conventions, Trouble, Top
@chapter GNU C++ library aims, objectives, and limitations

The GNU C++ library, libg++ is an attempt to provide a variety of C++
programming tools and other support to GNU C++ programmers.

Differences in distribution policy are only part of the difference
between libg++.a and AT&T libC.a.  libg++ is not intended to be an
exact clone of libC. For one, libg++ contains bits of code that depend
on special features of GNU g++ that are either different or lacking in
the AT&T version, including slightly different inlining and overloading
strategies, dynamic local arrays, etc.  All of these
differences are minor. For example, while the AT&T and GNU stream
classes are implemented in very different ways, the vast majority of
C++ programs compile and run under either version with no visible
difference. Additionally, all g++-specific constructs are conditionally
compiled; The library is designed to be compatible with any 2.0 C++
compiler.

libg++ has also contained workarounds for some limitations in g++: both
g++ and libg++ are still undergoing rapid development and testing---a
task that is helped tremendously by the feedback of active users.  This
manual is also still under development; it has some catching up to do
to include all the facilities now in the library.

libg++ is not the only freely available source of C++ class libraries.
Some notable alternative sources are Interviews and NIHCL.
(InterViews has been available on the X-windows X11 tapes and also
from interviews.stanford.edu.  NIHCL is available by anonymous
ftp from GNU archives (such as the pub directory of prep.ai.mit.edu),
although it is not supported by the FSF - and needs some work
before it will work with g++.)

As every C++ programmer knows, the design (moreso than the
implementation) of a C++ class library is something of a challenge.
Part of the reason is that C++ supports two, partially incompatible,
styles of object-oriented programming -- The "forest" approach,
involving a collection of free-standing classes that can be mixed and
matched, versus the completely hierarchical (smalltalk style)
approach, in which all classes are derived from a common ancestor.  Of
course, both styles have advantages and disadvantages.  So far, libg++
has adopted the "forest" approach.  Keith Gorlen's OOPS library adopts
the hierarchical approach, and may be an attractive alternative for C++
programmers who prefer this style.

Currently (and/or in the near future) libg++ provides support for a
few basic kinds of classes:

The first kind of support provides an interface between C++ programs and
C libraries. This includes basic header files (like @file{stdio.h}) as
well as things like the File and stream classes. Other classes that
interface to other aspects of C libraries (like those that maintain
environmental information) are in various stages of development; all
will undergo implementation modifications when the forthcoming GNU libc
library is released.

The second kind of support contains general-purpose basic classes that
transparently manage variable-sized objects on the freestore.  This
includes Obstacks, multiple-precision Integers and Rationals,
arbitrary length Strings, BitSets, and BitStrings.

Third, several classes and utilities of common interest (e.g.,
Complex numbers) are provided.

Fourth, a set of pseudo-generic prototype files are available
as a mechanism for generating common container classes. These
are described in more detail in the introduction to container
prototypes. Currently, only a textual substitution
mechanism is available for generic class creation.

@node Conventions, OK, General, Top
@chapter GNU C++ library stylistic conventions

@itemize @bullet

@item
C++ source files have file extension @file{.cc}. Both C-compatibility
header files and class declaration files have extension @file{.h}.

@item
C++ class names begin with capital letters, except for @code{istream}
and @code{ostream}, for AT&T C++ compatibility. Multi-word class
names capitalize each word, with no underscore separation.

@item 
Include files that define C++ classes begin with capital letters
(as do the names of the classes themselves).  @file{stream.h} is
uncapitalized for AT&T C++ compatibility.  

@item 
Include files that supply function prototypes for other C
functions (system calls and libraries) are all lower case.

@item 
All include files define a preprocessor variable _X_h, where X
is the name of the file, and conditionally compile only if this
has not been already defined. The @code{#pragma once} facility
is also used to avoid re-inclusion.

@item
Structures and objects that must be publicly defined,
but are not intended for public use have names beginning
with an underscore. (for example, the @code{_Srep} struct, which
is used only by the String and SubString classes.)

@item
The underscore is used to separate components of long function
names, @*e.g., @code{set_File_exception_handler()}.

@item
When a function could be usefully defined either as a
member or a friend, it is generally a member if it modifies
and/or returns itself, else it is a friend. There are cases
where naturalness of expression wins out over this rule.

@item
Class declaration files are formatted so that it is easy
to quickly check them to determine function names, parameters,
and so on. Because of the different kinds of things that may
appear in class declarations, there is no perfect way to do
this. Any suggestions on developing a common class
declaration formatting style are welcome.

@item
All classes use the same simple error (exception) handling strategy.
Almost every class has a member function named @code{error(char* msg)}
that invokes an associated error handler function via a pointer to that
function, so that the error handling function may be reset by
programmers. By default nearly all call @code{*lib_error_handler}, which
prints the message and then aborts execution. This system is subject
to change. In general, errors are assumed to be non-recoverable:
Library classes do not include code that allows graceful continuation
after exceptions.

@end itemize

@node OK, Proto, Conventions, Top
@chapter Support for representation invariants

Most GNU C++ library classes possess a method named @code{OK()},
that is useful in helping to verify correct performance of class
operations.

The @code{OK()} operations checks the ``representation invariant'' of a
class object. This is a test to check whether the object is in a valid
state. In effect, it is a (sometimes partial) verification of the
library's promise that (1) class operations always leave objects in
valid states, and (2) the class protects itself so that client functions
cannot corrupt this state.

While no simple validation technique can assure that all operations
perform correctly, calls to @code{OK()} can at least verify that
operations do not corrupt representations. For example for @code{String
a, b, c; ... a = b + c;}, a call to @code{a.OK();} will guarantee that
@code{a} is a valid @code{String}, but does not guarantee that it
contains the concatenation of @code{b + c}. However, given that @code{a}
is known to be valid, it is possible to further verify its properties,
for example via @code{a.after(b) == c && a.before(c) == b}. In other
words, @code{OK()} generally checks only those internal representation
properties that are otherwise inaccessible to users of the class. Other
class operations are often useful for further validation.

Failed calls to @code{OK()} call a class's @code{error} method if
one exists, else directly call @code{abort}. Failure indicates
an implementation error that should be reported.

With only rare exceptions, the internal support functions for a class
never themselves call @code{OK()} (although many of the test files
in the distribution call @code{OK()} extensively).

Verification of representational invariants can sometimes be
very time consuming for complicated data structures. 


@node Proto, Representations, OK, Top
@chapter Introduction to container class prototypes

As a temporary mechanism enabling the support of generic classes, the GNU
C++ Library distribution contains a directory (@file{g++-include}) of files
designed to serve as the basis for generating container classes of
specified elements.  These files can be used to generate @file{.h} and
@file{.cc} files in the current directory via a supplied shell script
program that performs simple textual substitution to create specific
classes.

While these classes are generated independently, and thus share no code,
it is possible to create versions that do share code among subclasses. For
example, using @code{typedef void* ent}, and then generating a
@code{entList} class, other derived classes could be created using the
@code{void*} coercion method described in Stroustrup, pp204-210.

This very simple class-generation facility is useful enough to serve
current purposes, but will be replaced with a more coherent mechanism for
handling C++ generics in a way that minimally disrupts current usage.
Without knowing exactly when or how parametric classes might be
added to the C++ language, provision of this simplest possible
mechanism, textual substitution, appears to be the safest strategy,
although it does require certain redundancies and awkward constructions.

Specific classes may be generated via the @file{genclass} shell script
program. This program has arguments specifying the kinds of base types(s)
to be used. Specifying base types requires two arguments. The first is the
name of the base type, which may be any named type, like @code{int} or
@code{String}. Only named types are supported; things like @code{int*} are
not accepted. However, pointers like this may be used by supplying the
appropriate typedefs (e.g., editing the resulting files to include
@code{typedef int* intp;}). The type name must be followed by one of the
words @code{val} or @code{ref}, to indicate whether the base elements
should be passed to functions by-value or by-reference. 

You can specify basic container classes using @code{genclass base
[val,ref] proto}, where @code{proto} is the name of the class being
generated.  Container classes like dictionaries and maps that require
two types may be specified via @code{genclass -2 keytype [val, ref],
basetype [val, ref] proto}, where the key type is specified first and
the contents type second.  The resulting classnames and filenames are
generated by prepending the specified type names to the prototype names,
and separating the filename parts with dots.  For example,
@code{genclass int val List} generates class @code{intList} residing in
files @file{int.List.h} and @file{int.List.cc}. @code{genclass -2 String
ref int val VHMap} generates (the awkward, but unavoidable) class name
@code{StringintVHMap}. Of course, programmers may use @code{typedef} or
simple editing to create more appropriate names.  The existence of dot
seperators in file names allows the use of GNU make to help automate
configuration and recompilation. An example Makefile exploiting such
capabilities may be found in the @file{libg++/proto-kit} directory.

The @code{genclass} utility operates via simple text substitution using
@code{sed}. All occurrences of the pseudo-types @code{<T>} and @code{<C>} 
(if there are two types) are replaced with the indicated type, and
occurrences of @code{<T&>} and @code{<C&>} are replaced by just the types,
if @code{val} is specified, or types followed by ``&'' if @code{ref} is
specified.

Programmers will frequently need to edit the @file{.h} file in order to
insert additional @code{#include} directives or other modifications.  A
simple utility, @file{prepend-header} to prepend other @file{.h} files
to generated files is provided in the distribution.  

One dubious virtue of the prototyping mechanism is that, because sources files,
not archived library classes, are generated, it is relatively simple for
programmers to modify container classes in the common case where slight
variations of standard container classes are required.

It is often a good idea for programmers to archive (via @code{ar})
generated classes into @file{.a} files so that only those class
functions actually used in a given application will be loaded.
The test subdirectory of the distribution shows an example of this.

Because of @code{#pragma interface} directives, the @file{.cc} files
should be compiled with @code{-O} or @code{-DUSE_LIBGXX_INLINES}
enabled.

Many container classes require specifications over and above the base
class type. For example, classes that maintain some kind of ordering of
elements require specification of a comparison function upon which to
base the ordering.  This is accomplished via a prototype file
@file{defs.hP} that contains macros for these functions. While these
macros default to perform reasonable actions, they can and should be
changed in particular cases. Most prototypes require only one or a few
of these. No harm is done if unused macros are defined to perform
nonsensical actions. The macros are:

@table @code

@item DEFAULT_INITIAL_CAPACITY
The initial capacity for containers (e.g., hash tables) that require 
an initial capacity argument for constructors. 
Default: 100

@item <T>EQ(a, b)
return true if a is considered equal to b for the purposes of
locating, etc., an element in a container. 
Default: (a == b)

@item <T>LE(a, b)
return true if a is less than or equal to b
Default: (a <= b)

@item <T>CMP(a, b)
return an integer < 0 if a<b, 0 if a==b, or > 0 if a>b.
Default: (a <= b)? (a==b)? 0 : -1 : 1

@item <T>HASH(a)
return an unsigned integer representing the hash of a.
Default: hash(a) ; where extern unsigned int hash(<T&>).
(note: several useful hash functions are declared in builtin.h
and defined in hash.cc)

@end table

Nearly all prototypes container classes support container
traversal via @code{Pix} pseudo indices, as described elsewhere.

All object containers must perform either a @code{X::X(X&)} (or
@code{X::X()} followed by @code{X::operator =(X&)}) to copy objects into
containers.  (The latter form is used for containers built from C++
arrays, like @code{VHSets}). When containers are destroyed, they invoke
@code{X::~X()}.  Any objects used in containers must have well behaved
constructors and destructors. If you want to create containers that
merely reference (point to) objects that reside elsewhere, and are not
copied or destroyed inside the container, you must use containers
of pointers, not containers of objects.

All prototypes are designed to generate @emph{HOMOGENOUS} container
classes.  There is no universally applicable method in C++ to support
heterogenous object collections with elements of various subclasses of
some specified base class. The only way to get heterogenous structures
is to use collections of pointers-to-objects, not collections of objects
(which also requires you to take responsibility for managing storage for
the objects pointed to yourself).

For example, the following usage illustrates a commonly encountered
danger in trying to use container classes for heterogenous structures:

@smallexample
class Base @{ int x; ...@}
class Derived : public Base @{ int y; ... @}

BaseVHSet s; // class BaseVHSet generated via something like
             // `genclass Base ref VHSet'

void f()
@{
  Base b;
  s.add(b); // OK

  Derived d;
  s.add(d);  // (CHOP!)
@}
@end smallexample

At the line flagged with @samp{(CHOP!)}, a @code{Base::Base(Base&)} is
called inside @code{Set::add(Base&)}---@emph{not}
@code{Derived::Derived(Derived&)}.  Actually, in @code{VHSet}, a
@code{Base::operator =(Base&)}, is used instead to place the element in
an array slot, but with the same effect.  So only the Base part is
copied as a @code{VHSet} element (a so-called chopped-copy). In this
case, it has an @code{x} part, but no @code{y} part; and a Base, not
Derived, vtable. Objects formed via chopped copies are rarely
sensible.@refill

To avoid this, you must resort to pointers:

@smallexample
typedef Base* BasePtr;

BasePtrVHSet s; // class BaseVHSet generated via something like
                // `genclass BasePtr val VHSet'

void f()
@{
  Base* bp = new Base;
  s.add(b);

  Base* dp = new Derived;
  s.add(d);  // works fine.

  // Don't forget to delete bp and dp sometime.
  // The VHSet won't do this for you.
@}
@end smallexample

@section Example

The prototypes can be difficult to use on first attempt. Here is an
example that may be helpful. The utilities in the @file{proto-kit}
simplify much of the actions described, but are not used here.

Suppose you create a class @code{Person}, and want to make an Map that
links the social security numbers associated with each person. You start
off with a file @file{Person.h}

@example

#include <String.h>

class Person
@{
  String nm;
  String addr;
  //...
public:
  const String& name() @{ return nm; @}
  const String& address() @{ return addr; @}
  void          print() @{ ... @}
  //...
@}

@end example

And in file @file{SSN.h},

@example
typedef unsigned int SSN;
@end example

Your first decision is what storage/usage strategy to use. There are
several reasonable alternatives here: You might create an ``object
collection'' of Persons, a ``pointer collection'' of
pointers-to-Persons, or even a simple String map, housing either copies
of pointers to the names of Persons, since other fields are unused for
purposes of the Map. In an object collection, instances of class Person
``live'' inside the Map, while in a pointer collection, the instances
live elsewhere. Also, as above, if instances of subclasses of Person are
to be used inside the Map, you must use pointers. In a String Map, the
same difference holds, but now only for the name fields. Any of these
choices might make sense in particular applications. 

The second choice is the Map implementation strategy. Either a tree
or a hash table might make sense. Suppose you want an AVL tree Map.
There are two things to now check. First, as an object collection,
the AVLMap requires that the elsement class contain an @code{X(X&)}
constructor. In C++, if you don't specify such a constructor, one
is constructed for you, but it is a very good idea to always do this
yourself, to avoid surprises. In this example, you'd use something like
@example
class Person 
@{ ...; 
    Person(const Person& p) :nm(p.nm), addr(p.addr) @{@}
@};
@end example

Also, an AVLMap requires a comparison function for elements in order
to maintain order. Rather than requiring you to write a particular
comparison function, a @file{defs} file is consulted to determine how to
compare items. You must create and edit such a file.

Before creating @file{Person.defs.h}, you must first make one additional
decision. Should the Map member functions like @code{m.contains(p)}
take arguments (@code{p}) by reference (i.e., typed as 
@code{int Map::contains(const Person& p)} or by value (i.e., typed as
@code{int Map::contains(const Person p)}. Generally, for user-defined
classes, you want to pass by reference, and for builtins and pointers,
to pass by value. SO you should pick by-reference.

You can now create @file{Person.defs.h} via @code{genclass Person ref defs}.
This creates a simple skeleton that you must edit. First, add
@code{#include "Person.h"} to the top. Second, edit the @code{<T>CMP(a,b)}
macro to compare on name, via

@example
#define <T>CMP(a, b) ( compare(a.name(), b.name()) )
@end example

@noindent
which invokes the @code{int compare(const String&, const String&)}
function from @file{String.h}. Of course, you could define this in any
other way as well. In fact, the default versions in the skeleton turn
out to be OK (albeit inefficient) in this particular example.

You may also want to create file @file{SSN.defs.h}. Here, choosing
call-by-value makes sense, and since no other capabilities (like
comparison functions) of the SSNs are used (and the defaults are OK
anyway), you'd type

@example
genclass SSN val defs
@end example

@noindent
and then edit to place @code{#include "SSN.h"} at the top.

Finally, you can generate the classes. First, generate the base
class for Maps via

@example
genclass -2 Person ref SSN val Map
@end example

@noindent
This generates only the abstract class, not the implementation, in file
@file{Person.SSN.Map.h} and @file{Person.SSN.Map.cc}.  To create the
AVL implementation, type

@example
genclass -2 Person ref SSN val AVLMap
@end example

@noindent
This creates the class @code{PersonSSNAVLMap}, in
@file{Person.SSN.AVLMap.h} and @file{Person.SSN.AVLMap.cc}.

To use the AVL implementation, compile the two generated @file{.cc} files, and
specify @samp{#include "Person.SSN.AVLMap.h"} in the application program.
All other files are included in the right ways automatically.

One last consideration, peculiar to Maps, is to pick a reasonable
default contents when declaring an AVLMap. Zero might be appropriate
here, so you might declare a Map,

@example
PersonSSNAVLMap m((SSN)0);
@end example

Suppose you wanted a @code{VHMap} instead of an @code{AVLMap} Besides
generating different implementations, there are two differences in
how you should prepare the @file{defs} file. First, because a VHMap
uses a C++ array internally, and because C++ array slots are initialized
differently than single elements, you must ensure that class Person
contains (1) a no-argument constructor, and (2) an assignment operator.
You could arrange this via

@smallexample
class Person 
@{ ...; 
    Person() @{@}
  void operator = (const Person& p) @{ nm = p.nm; addr = p.addr; @}
@};
@end smallexample

(The lack of action in the constructor is OK here because @code{Strings}
possess usable no-argument constructors.)

You also need to edit @file{Person.defs.h} to indicate a usable hash
function and default capacity, via something like

@example
#include <builtin.h>
#define <T>HASH(x)  (hashpjw(x.name().chars()))
#define DEFAULT_INITIAL_CAPACITY 1000
@end example

Since the @code{hashpjw} function from @file{builtin.h} is
appropriate here. Changing the default capacity to a value
expected to exceed the actual capacity helps to avoid
``hidden'' inefficiencies when a new VHMap is created without
overriding the default, which is all too easy to do.

Otherwise, everything is the same as above, substituting
@code{VHMap} for @code{AVLMap}.

@node Representations, Expressions, Proto, Top
@chapter Variable-Sized Object Representation

One of the first goals of the GNU C++ library is to enrich the kinds of
basic classes that may be considered as (nearly) ``built into'' C++. A good
deal of the inspiration for these efforts is derived from considering
features of other type-rich languages, particularly Common Lisp and Scheme.
The general characteristics of most class and friend operators and
functions supported by these classes has been heavily influenced
by such languages.

Four of these types, Strings, Integers, BitSets, and BitStrings (as well as
associated and/or derived classes) require representations suitable for
managing variable-sized objects on the free-store. The basic technique used
for all of these is the same, although various details necessarily differ
from class to class.

The general strategy for representing such objects is to create chunks of
memory that include both header information (e.g., the size of the object),
as well as the variable-size data (an array of some sort) at the end
of the chunk. Generally the maximum size of an object is limited to
something less than all of addressable memory, as a safeguard. The minimum
size is also limited so as not to waste allocations expanding very small
chunks. Internally, chunks are allocated in blocks well-tuned to the
performance of the @code{new} operator.

Class elements themselves are merely pointers to these chunks.
Most class operations are performed via inline ``translation''
functions that perform the required operation on the corresponding
representation. However, constructors and assignments operate by
copying entire representations, not just pointers.


No attempt is made to control temporary creation in expressions
and functions involving these classes. Users of previous versions
of the classes will note the disappearance of both ``Tmp'' classes
and reference counting. These were dropped because, while they
did improve performance in some cases, they obscure class
mechanics, lead programmers into the false belief that they need not
worry about such things, and occasionally have paradoxical behavior.


These variable-sized object classes are integrated as well as possible
into C++. Most such classes possess converters that allow automatic
coercion both from and to builtin basic types. (e.g., char* to and from
String, long int to and from Integer, etc.). There are pro's and con's
to circular converters, since they can sometimes lead to the conversion
from a builtin type through to a class function and back to a builtin
type without any special attention on the part of the programmer, both
for better and worse.

Most of these classes also provide special-case operators and functions
mixing basic with class types, as a way to avoid constructors in cases
where the operations do not rely on anything special about the
representations.  For example, there is a special case concatenation
operator for a String concatenated with a char, since building the
result does not rely on anything about the String header. Again, there
are arguments both for and against this approach. Supporting these cases
adds a non-trivial degree of (mainly inline) function proliferation, but
results in more efficient operations. Efficiency wins out over parsimony
here, as part of the goal to produce classes that provide sufficient
functionality and efficiency so that programmers are not tempted to try
to manipulate or bypass the underlying representations.

@node Expressions, Pix, Representations,  Top
@chapter Some guidelines for using expression-oriented classes


The fact that C++ allows operators to be overloaded for user-defined
classes can make programming with library classes like @code{Integer},
@code{String}, and so on very convenient. However, it is worth
becoming familiar with some of the inherent limitations and problems
associated with such operators.

Many operators are @emph{constructive}, i.e., create a new object
based on some function of some arguments. Sometimes the creation
of such objects is wasteful. Most library classes supporting
expressions contain facilities that help you avoid such waste.

For example, for @code{Integer a, b, c; ...;  c = a + b + a;}, the
plus operator is called to sum a and b, creating a new temporary object
as its result. This temporary is then added with a, creating another
temporary, which is finally copied into c, and the temporaries are then
deleted. In other words, this code might have an effect similar to
@code{Integer a, b, c; ...; Integer t1(a); t1 += b; Integer t2(t1);
t2 += a; c = t2;}.

For small objects, simple operators, and/or non-time/space critical
programs, creation of temporaries is not a big problem. However, often,
when fine-tuning a program, it may be a good idea to rewrite such
code in a less pleasant, but more efficient manner.

For builtin types like ints, and floats, C and C++ compilers already
know how to optimize such expressions to reduce the need for
temporaries. Unfortunately, this is not true for C++ user defined
types, for the simple (but very annoying, in this context) reason that
nothing at all is guaranteed about the semantics of overloaded operators
and their interrelations. For example, if the above expression just
involved ints, not Integers, a compiler might internally convert the
statement into something like @code{ c += a; c += b; c+= a; }, or
perhaps something even more clever.  But since C++ does not know that
Integer operator += has any relation to Integer operator +, A C++
compiler cannot do this kind of expression optimization itself.

In many cases, you can avoid construction of temporaries simply by
using the assignment versions of operators whenever possible, since
these versions create no temporaries. However, for maximum flexibility,
most classes provide a set of ``embedded assembly code'' procedures
that you can use to fully control time, space, and evaluation strategies.
Most of these procedures are ``three-address'' procedures that take
two @code{const} source arguments, and a destination argument. The
procedures perform the appropriate actions, placing the results in
the destination (which is may involve overwriting old contents). These
procedures are designed to be fast and robust. In particular, aliasing
is always handled correctly, so that, for example
@code{add(x, x, x); } is perfectly OK. (The names of these procedures
are listed along with the classes.)

For example, suppose you had an Integer expression
@code{ a = (b - a) * -(d / c); }

This would be compiled as if it were
@code{ Integer t1=b-a; Integer t2=d/c; Integer t3=-t2; Integer t4=t1*t3; a=t4;}

But, with some manual cleverness, you might yourself some up with
@code{ sub(a, b, a); mul(a, d, a); div(a, c, a); }


A related phenomenon occurs when creating your own constructive
functions returning instances of such types. Suppose you wanted
to write function 
@code{Integer f(const Integer& a) @{ Integer r = a;  r += a; return r; @}}

This function, when called (as in @code{ a = f(a); }) demonstrates a 
similar kind of wasted copy. The returned value r must be copied
out of the function before it can be used by the caller. In GNU
C++, there is an alternative via the use of named return values.
Named return values allow you to manipulate the returned object
directly, rather than requiring you to create a local inside
a function and then copy it out as the returned value. In this
example, this can be done via
@code{Integer f(const Integer& a) return r(a) @{ r += a; return; @}}


A final guideline: The overloaded operators are very convenient, and
much clearer to use than procedural code. It is almost always a good
idea to make it right, @emph{then} make it fast, by translating 
expression code into procedural code after it is known to be correct.



@node Pix, Headers, Expressions, Top
@chapter Pseudo-indexes

Many useful classes operate as containers of elements. Techniques for
accessing these elements from a container differ from class to class.
In the GNU C++ library, access methods have been partially standardized
across different classes via the use of pseudo-indexes called
@code{Pixes}.  A @code{Pix} acts in some ways like an index, and in some
ways like a pointer. (Their underlying representations are just
@code{void*} pointers). A @code{Pix} is a kind of ``key'' that is
translated into an element access by the class.  In virtually all cases,
@code{Pixes} are pointers to some kind internal storage cells. The
containers use these pointers to extract items.

@code{Pixes} support traversal and inspection of elements in a
collection using analogs of array indexing. However, they are
pointer-like in that @code{0} is treated as an invalid @code{Pix}, and
unsafe insofar as programmers can attempt to access nonexistent elements
via dangling or otherwise invalid @code{Pixes} without first checking
for their validity. 

In general it is a very bad idea to perform traversals in the the midst
of destructive modifications to containers.

Typical applications might include code using the idiom
@example
for (Pix i = a.first(); i != 0; a.next(i)) use(a(i));
@end example
for some container @code{a} and function @code{use}.

Classes supporting the use of @code{Pixes} always contain the following 
methods, assuming a container @code{a} of element types of @code{Base}.

@table @code

@item Pix i = a.first()
Set i to index the first element of a or 0 if a is empty.

@item a.next(i)
advance i to the next element of a or 0 if there is no next element;

@item Base x = a(i); a(i) = x;
a(i) returns a reference to the element indexed by i.

@item int present = a.owns(i)
returns true if Pix i is a valid Pix in a. This is often a
relatively slow operation, since the collection must usually 
traverse through elements to see if any correspond to the Pix.

@end table

Some container classes also support backwards traversal via

@table @code
@item Pix i = a.last()
Set i to the last element of a or 0 if a is empty.

@item a.prev(i)
sets i to the previous element in a, or 0 if there is none.
@end table

Collections supporting elements with an equality operation possess

@table @code
@item Pix j = a.seek(x)
sets j to the index of the first occurrence of x, or 0 if x is 
not contained in a.
@end table

Bag classes possess

@table @code
@item Pix j = a.seek(x, Pix from = 0)
sets j to the index of the next occurrence of x following i,
or 0 if x is not contained in a. If i == 0, the first occurrence 
is returned.
@end table

Set, Bag, and PQ classes possess

@table @code
@item Pix j = a.add(x) (or a.enq(x) for priority queues)
add x to the collection, returning its Pix. The Pix of an item
can change in collections where further additions and deletions
involve the actual movement of elements (currently in OXPSet,
OXPBag, XPPQ, VOHSet), but in all other cases, an item's Pix may
be considered a permanent key to its location.
@end table

@node Headers, Builtin, Pix, Top
@chapter Header files for interfacing C++ to C

The following files are provided so that C++ programmers may
invoke common C library and system calls. The names and contents
of these files are subject to change in order to be compatible
with the forthcoming GNU C library. Other files, not listed
here, are simply C++-compatible interfaces to corresponding C
library files.

@table @file
@item values.h
A collection of constants defining the numbers of bits in builtin
types, minimum and maximum values, and the like. Most names are
the same as those found in @file{values.h} found on Sun systems.

@item std.h
A collection of common system calls and @file{libc.a} functions.
Only those functions that can be declared without introducing
new type definitions (socket structures, for example) are
provided. Common @code{char*} functions (like @code{strcmp}) are among
the declarations. All functions are declared along with their
library names, so that they may be safely overloaded.

@item string.h
This file merely includes @file{<std.h>}, where string function
prototypes are declared. This is a workaround for the fact that
system @file{string.h} and @file{strings.h} files often differ
in contents.

@item osfcn.h
This file merely includes @file{<std.h>}, where system function
prototypes are declared. 

@item libc.h
This file merely includes @file{<std.h>}, where C library function
prototypes are declared. 

@item math.h
A collection of prototypes for functions usually found in
libm.a, plus some @code{#define}d constants that appear to be
consistent with those provided in the AT&T version. The value
of @code{HUGE} should be checked before using. Declarations of
all common math functions are preceded with @code{overload}
declarations, since these are commonly overloaded.

@item stdio.h
Declaration of @code{FILE} (@code{_iobuf}), common macros (like
@code{getc}), and function prototypes for @file{libc.a}
functions that operate on @code{FILE*}'s. The value
@code{BUFSIZ} and the declaration of @code{_iobuf} should be
checked before using.

@item assert.h
C++ versions of assert macros.

@item generic.h
String concatenation macros useful in creating generic classes.
They are similar in function to the AT&T CC versions.

@item new.h
Declarations of the default global operator new, the two-argument
placement version, and associated error handlers.
@end table

@node Builtin, New, Headers, Top
@chapter Utility functions for built in types

Files @file{builtin.h} and corresponding @file{.cc} implementation
files contain various convenient
inline and non-inline utility functions. These include useful
enumeration types, such as @code{TRUE}, @code{FALSE} ,the type
definition for pointers to libg++ error handling functions, and
the following functions.

@table @code
@item long abs(long x); double abs(double x);
inline versions of abs. Note that the standard libc.a version,
@code{int abs(int)} is @emph{not} declared as inline.

@item void clearbit(long& x, long b);
clears the b'th bit of x (inline).

@item void setbit(long& x, long b);
sets the b'th bit of x (inline)

@item int testbit(long x, long b);
returns the b'th bit of x (inline).

@item int even(long y);
returns true if x is even (inline).

@item int odd(long y);
returns true is x is odd (inline).

@item int sign(long x); int sign(double x);
returns -1, 0, or 1, indicating whether x is less than, equal to, or
greater than zero (inline).

@item long gcd(long x, long y);
returns the greatest common divisor of x and y.

@item long lcm(long x, long y);
returns the least common multiple of x and y.

@item long lg(long x); 
returns the floor of the base 2 log of x.

@item long pow(long x, long y); double pow(double x, long y);
returns x to the integer power y using via the iterative O(log y)
``Russian peasant'' method.

@item long sqr(long x); double sqr(double x);
returns x squared (inline).

@item long sqrt(long y);
returns the floor of the square root of x.

@item unsigned int hashpjw(const char* s);
a hash function for null-terminated char* strings using the
method described in Aho, Sethi, & Ullman, p 436.

@item unsigned int multiplicativehash(int x);
a hash function for integers that returns the lower bits of 
multiplying x by the golden ratio times pow(2, 32). 
See Knuth, Vol 3, p 508.

@item unsigned int foldhash(double x);
a hash function for doubles that exclusive-or's the first and
second words of x, returning the result as an integer.

@item double start_timer()
Starts a process timer.

@item double return_elapsed_time(double last_time)
Returns the process time since last_time. 
If last_time == 0 returns the time since the last start_timer. 
Returns -1 if start_timer was not first called.

@end table

File @file{Maxima.h} includes versions of @code{MAX, MIN}
for builtin types.

File @file{compare.h} includes versions of @code{compare(x, y)}
for builtin types. These return negative if the first argument
is less than the second, zero for equal, and positive for greater.

@node New, Stream, Builtin, Top
@chapter Library dynamic allocation primitives

Libg++ contains versions of @code{malloc, free, realloc} that were
designed to be well-tuned to C++ applications. The source file
@file{malloc.c} contains some design and implementation details.
Here are the major user-visible differences from most system
malloc routines:

@enumerate

@item
These routines @emph{overwrite} storage of freed space. This
means that it is never permissible to use a @code{delete}'d
object in any way. Doing so will either result in trapped
fatal errors or random aborts within malloc, free, or realloc.

@item
The routines tend to perform well when a large number
of objects of the same size are allocated and freed. You
may find that it is not worth it to create your
own special allocation schemes in such cases.

@item
The library sets top-level @code{operator new()} to call malloc and
@code{operator delete()} to call free. Of course, you may override these
definitions in C++ programs by creating your own operators that will
take precedence over the library versions. However, if you do so, be
sure to define @emph{both} @code{operator new()} and @code{operator
delete()}.

@item
These routines do @emph{not} support the odd convention, maintained by
some versions of malloc, that you may call @code{realloc} with a pointer
that has been @code{free}'d.

@item
The routines automatically perform simple checks on @code{free}'d
pointers that can often determine whether users have accidentally
written beyond the boundaries of allocated space, resulting in a fatal
error.

@item
The function @code{malloc_usable_size(void* p)} returns the number of
bytes actually allocated for @code{p}. For a valid pointer (i.e., one
that has been @code{malloc}'d or @code{realloc}'d but not yet
@code{free}'d) this will return a number greater than or equal to the
requested size, else it will normally return 0. Unfortunately, a
non-zero return can not be an absolutely perfect indication of lack of
error. If a chunk has been @code{free}'d but then re-allocated for a
different purpose somewhere elsewhere, then @code{malloc_usable_size}
will return non-zero. Despite this, the function can be very valuable
for performing run-time consistency checks.

@item
@code{malloc} requires 8 bytes of overhead per allocated chunk, plus a
mmaximum alignment adjustment of 8 bytes. The number of bytes of usable
space is exactly as requested, rounded to the nearest 8 byte boundary.

@item
The routines do @emph{not} contain any synchronization support for
multiprocessing. If you perform global allocation on a shared
memory multiprocessor, you should disable compilation and use
of libg++ malloc in the distribution @file{Makefile} and use your
system version of malloc.

@end enumerate

@iftex
@node IOStream
@chapter The new input/output classes

The iostream classes implement most of the features of AT&T
version 2.0 iostream library classes, and most of the features
of the ANSI X3J16 library draft (which is based on the AT&T design).
These classes are available in @code{libg++} for convenience and for
compatibility with older releases; however, since the iostream classes
are licensed under less stringent terms than @code{libg++}, they are now
also available in a separate library called @code{libio}---and
documented in a separate manual, corresponding to that library.

@xref{Introduction,,Introduction, iostream.info, The GNU C++ Iostream
Library}.
@end iftex

@node Stream, Obstack, New, Top
@chapter The old I/O library

WARNING: This chapter describes classes that are @emph{obsolete}.
These classes are normally not available when libg++
is installed normally.  The sources are currently included
in the distribution, and you can configure libg++ to use
these classes instead of the new iostream classes.
This is only a temporary measure; you should convert your
code to use iostreams as soon as possible.  The iostream
classes provide some compatibility support, but it is
very incomplete (there is no longer a @code{File} class).

@section File-based classes
   
The @code{File} class supports basic IO on Unix files.  Operations are
based on common C stdio library functions.

@code{File} serves as the base class for istreams, ostreams, and other
derived classes. It contains the interface between the Unix stdio file
library and these more structured classes.  Most operations are implemented
as simple calls to stdio functions. @code{File} class operations are also fully
compatible with raw system file reads and writes (like the system
@code{read} and @code{lseek} calls) when buffering is disabled (see below).
The @code{FILE*} stdio file pointer is, however maintained as protected.
Classes derived from File may only use the IO operations provided by File,
which encompass essentially all stdio capabilities.

The class contains four general kinds of functions: methods for binding
@code{File}s to physical Unix files, basic IO methods, file and buffer
control methods, and methods for maintaining logical and physical file
status.


Binding and related tasks are accomplished via @code{File} constructors and
destructors, and member functions @code{open, close, remove, filedesc,
name, setname}.

If a file name is provided in a constructor or open, it is
maintained as class variable @code{nm} and is accessible
via @code{name}.  If no name is provided, then @code{nm} remains
null, except that @code{Files} bound to the default files stdin,
stdout, and stderr are automatically given the names
@code{(stdin), (stdout), (stderr)} respectively.  
The function @code{setname} may be used to change the
internal name of the @code{File}. This does not change the name
of the physical file bound to the File.
      
The member function @code{close} closes a file.  The
@code{~File} destructor closes a file if it is open, except
that stdin, stdout, and stderr are flushed but left open for
the system to close on program exit since some systems may
require this, and on others it does not matter.  @code{remove}
closes the file, and then deletes it if possible by calling the
system function to delete the file with the name provided in
the @code{nm} field.

@section Basic IO

@itemize @bullet

@item 
@code{read} and @code{write} perform binary IO via stdio
@code{fread} and @code{fwrite}.

@item 
@code{get} and @code{put} for chars invoke stdio @code{getc}
and @code{putc} macros.

@item 
@code{put(const char* s)} outputs a null-terminated string via
stdio @code{fputs}.

@item 
@code{unget} and @code{putback} are synonyms.  Both call stdio
@code{ungetc}.

@end itemize

@section File Control

@code{flush}, @code{seek}, @code{tell}, and @code{tell} call the
corresponding stdio functions.

@code{flush(char)} and @code{fill()} call stdio @code{_flsbuf}
and @code{_filbuf} respectively.

@code{setbuf} is mainly useful to turn off buffering in cases
where nonsequential binary IO is being performed. @code{raw} is a
synonym for @code{setbuf(_IONBF)}.  After a @code{f.raw()}, using
the stdio functions instead of the system @code{read, write},
etc., calls entails very little overhead.  Moreover, these become
fully compatible with intermixed system calls (e.g.,
@code{lseek(f.filedesc(), 0, 0)}). While intermixing @code{File}
and system IO calls is not at all recommended, this technique
does allow the @code{File} class to be used in conjunction with
other functions and libraries already set up to operate on file
descriptors. @code{setbuf} should be called at most once after a
constructor or open, but before any IO.

@section File Status

File status is maintained in several ways. 

A @code{File} may be checked for accessibility via
@code{is_open()}, which returns true if the File is bound to a
usable physical file, @code{readable()}, which returns true if
the File can be read from (opened for reading, and not in a
_fail state), or @code{writable()}, which returns true if the
File can be written to.

@code{File} operations return their status via two means: failure and
success are represented via the logical state. Also, the
return values of invoked stdio and system functions that
return useful numeric values (not just failure/success flags)
are held in a class variable accessible via @code{iocount}.
(This is useful, for example, in determining the number of
items actually read by the @code{read} function.)

Like the AT&T i/o-stream classes, but unlike the description in
the Stroustrup book, p238, @code{rdstate()} returns the bitwise
OR of @code{_eof}, @code{_fail} and @code{_bad}, not necessarily
distinct values. The functions @code{eof()}, @code{fail()},
@code{bad()}, and @code{good()} can be used to test for each of
these conditions independently.

@code{_fail} becomes set for any input operation that could not
read in the desired data, and for other failed operations. As
with all Unix IO, @code{_eof} becomes true only when an input
operations fails because of an end of file. Therefore,
@code{_eof} is not immediately true after the last successful
read of a file, but only after one final read attempt. Thus, for
input operations, @code{_fail} and @code{_eof} almost always
become true at the same time.  @code{bad} is set for unbound
files, and may also be set by applications in order to communicate
input corruption. Conversely, @code{_good} is defined as 0 and
is returned by @code{rdstate()} if all is well.

The state may be modified via @code{clear(flag)}, which,
despite its name, sets the corresponding state_value flag.
@code{clear()} with no arguments resets the state to @code{_good}.
@code{failif(int cond)} sets the state to @code{_fail} only if
@code{cond} is true.  

Errors occuring during constructors and file opens also invoke the
function @code{error}.  @code{error} in turn calls a resetable error
handling function pointed to by the non-member global variable
@code{File_error_handler} only if a system error has been generated.
Since @code{error} cannot tell if the current system error is actually
responsible for a failure, it may at times print out spurious messages.
Three error handlers are provided. The default,
@code{verbose_File_error_handler} calls the system function
@code{perror} to print the corresponding error message on standard
error, and then returns to the caller.  @code{quiet_File_error_handler}
does nothing, and simply returns.  @code{fatal_File_error_handler}
prints the error and then aborts execution. These three handlers, or any
other user-defined error handlers can be selected via the non-member
function @code{set_File_error_handler}.

All read and write operations communicate either logical or
physical failure by setting the @code{_fail} flag.  All further
operations are blocked if the state is in a @code{_fail} or@code{_bad}
condition. Programmers must explicitly use @code{clear()} to
reset the state in order to continue IO processing after
either a logical or physical failure.  C programmers who are
unfamiliar with these conventions should note that, unlike
the stdio library, @code{File} functions indicate IO success,
status, or failure solely through the state, not via return values of
the functions.  The @code{void*} operator or @code{rdstate()}
may be used to test success.  In particular, according to c++
conversion rules, the @code{void*} coercion is automatically
applied whenever the @code{File&} return value of any @code{File}
function is tested in an @code{if} or @code{while}.  Thus,
for example, an easy way to copy all of stdin to stdout until
eof (at which point @code{get} fails) or some error is
@code{char c; while(cin.get(c) && cout.put(c));}.

@ignore
@section The istream and ostream classes

Some of these are supported by incorporating additional,
mainly virtual, functions into streambufs:

@table @code

@item streambuf::open([various args])
attaches the streambuf to a file, if applicable

@item streambuf::close()
detaches the streambuf from a file, if applicable.

@item streambuf::sputs(const char* s)
outputs null-terminated string s in a generally faster way
than repeated @code{sputcs}.

@item streambuf::sputsn(const char* s, int n)
outputs the first n characters of s in a generally faster way
than repeated @code{sputcs}.

@end table
@end ignore

The current version of istreams and ostreams differs significantly
from previous versions in order to obtain compatibility with
AT&T 1.2 streams. Most code using previous versions should still
work. However, the following features of @code{File} are not
incorporated in streams (they are still present in @code{File}):
@code{scan(const char* fmt...), remove(), read(), write(),
setbuf(), raw()}. Additionally, the feature of previous streams
that allowed free intermixing of stream and stdio input and output
is no longer guaranteed to always behave as desired.

@node Obstack, AllocRing, Stream, Top
@chapter The Obstack class


The @code{Obstack} class is a simple rewrite of the C obstack macros and
functions provided in the GNU CC compiler source distribution.  

Obstacks provide a simple method of creating and maintaining a string
table, optimized for the very frequent task of building strings
character-by-character, and sometimes keeping them, and sometimes
not. They seem especially useful in any parsing application. One of the
test files demonstrates usage.

A brief summary:
@table @code

@item grow   
places something on the obstack without committing to wrap 
it up as a single entity yet.

@item finish 
wraps up a constructed object as a single entity, 
and returns the pointer to its start address.

@item copy   
places things on the obstack, and @emph{does} wrap them up.
@code{copy} is always equivalent to first grow, then finish.

@item free   
deletes something, and anything else put on the obstack since its creation.
@end table

The other functions are less commonly needed:
@table @code
@item blank
is like grow, except it just grows the space by size units
without placing anything into this space
@item alloc
is like @code{blank}, but it wraps up the object and returns its starting
address. 
@item chunk_size, base, next_free, alignment_mask, size, room
returns the appropriate class variables.
@item grow_fast
places a character on the obstack without checking if there is enough room.
@item blank_fast
like @code{blank}, but without checking if there is enough room.
@item shrink(int n)
shrink the current chunk by n bytes.
@item contains(void* addr)
returns true if the Obstack holds the address addr.
@end table

Here is a lightly edited version of the original C documentation:

These functions operate a stack of objects.  Each object starts life
small, and may grow to maturity.  (Consider building a word syllable
by syllable.)  An object can move while it is growing.  Once it has
been ``finished'' it never changes address again.  So the ``top of the
stack'' is typically an immature growing object, while the rest of the
stack is of mature, fixed size and fixed address objects.

These routines grab large chunks of memory, using the GNU C++ @code{new}
operator.  On occasion, they free chunks, via @code{delete}.

Each independent stack is represented by a Obstack.

One motivation for this package is the problem of growing char strings
in symbol tables.  Unless you are a ``fascist pig with a read-only mind''
[Gosper's immortal quote from HAKMEM item 154, out of context] you
would not like to put any arbitrary upper limit on the length of your
symbols.

In practice this often means you will build many short symbols and a
few long symbols.  At the time you are reading a symbol you don't know
how long it is.  One traditional method is to read a symbol into a
buffer, @code{realloc()}ating the buffer every time you try to read a
symbol that is longer than the buffer.  This is beaut, but you still will
want to copy the symbol from the buffer to a more permanent
symbol-table entry say about half the time.

With obstacks, you can work differently.  Use one obstack for all symbol
names.  As you read a symbol, grow the name in the obstack gradually.
When the name is complete, finalize it.  Then, if the symbol exists already,
free the newly read name.

The way we do this is to take a large chunk, allocating memory from
low addresses.  When you want to build a symbol in the chunk you just
add chars above the current ``high water mark'' in the chunk.  When you
have finished adding chars, because you got to the end of the symbol,
you know how long the chars are, and you can create a new object.
Mostly the chars will not burst over the highest address of the chunk,
because you would typically expect a chunk to be (say) 100 times as
long as an average object.

In case that isn't clear, when we have enough chars to make up
the object, @emph{they are already contiguous in the chunk} (guaranteed)
so we just point to it where it lies.  No moving of chars is
needed and this is the second win: potentially long strings need
never be explicitly shuffled. Once an object is formed, it does not
change its address during its lifetime.

When the chars burst over a chunk boundary, we allocate a larger
chunk, and then copy the partly formed object from the end of the old
chunk to the beginning of the new larger chunk.  We then carry on
accreting characters to the end of the object as we normally would.

A special version of grow is provided to add a single char at a time
to a growing object.

Summary:

@itemize @bullet
@item 
We allocate large chunks.
@item 
We carve out one object at a time from the current chunk.
@item 
Once carved, an object never moves.
@item 
We are free to append data of any size to the currently growing object.
@item 
Exactly one object is growing in an obstack at any one time.
@item 
You can run one obstack per control block.
@item 
You may have as many control blocks as you dare.
@item 
Because of the way we do it, you can `unwind' a obstack back to a
previous state. (You may remove objects much as you would with a stack.)
@end itemize

The obstack data structure is used in many places in the GNU C++ compiler.

Differences from the the GNU C version
@enumerate
@item 
The obvious differences stemming from the use of classes and
inline functions instead of structs and macros. The C
@code{init} and @code{begin} macros are replaced by constructors.

@item 
Overloaded function names are used for grow (and others),
rather than the C @code{grow}, @code{grow0}, etc.

@item 
All dynamic allocation uses the the built-in @code{new} operator.
This restricts flexibility by a little, but maintains compatibility
with usual C++ conventions. 

@item 
There are now two versions of finish:

@enumerate
@item 
finish() behaves like the C version.

@item 
finish(char terminator) adds @code{terminator}, and then calls
@code{finish()}.  This enables the normal invocation of @code{finish(0)} to
wrap up a string being grown character-by-character.
@end enumerate

@item 
There are special versions of grow(const char* s) and 
copy(const char* s) that add the null-terminated string @code{s}
after computing its length.

@item
The shrink and contains functions are provided.

@end enumerate

@node AllocRing, String, Obstack, Top
@chapter The AllocRing class

An AllocRing is a bounded ring (circular list), each of whose elements
contains a pointer to some space allocated via @code{new
char[some_size]}. The entries are used cyclicly.  The size, n, of the
ring is fixed at construction. After that, every nth use of the ring
will reuse (or reallocate) the same space. AllocRings are needed in
order to temporarily hold chunks of space that are needed transiently,
but across constructor-destructor scopes. They mainly useful for storing
strings containing formatted characters to print across various
functions and coercions. These strings are needed across routines, so
may not be deleted in any one of them, but should be recovered at some
point. In other words, an AllocRing is an extremely simple minded
garbage collection mechanism. The GNU C++ library used to use one
AllocRing for such formatting purposes, but it is being phased out,
and is now only used by obsolete functions.
These days, AllocRings are probably not very useful.

Support includes:

@table @code

@item AllocRing a(int n)
constructs an Alloc ring with n entries, all null.

@item void* mem = a.alloc(sz)
moves the ring pointer to the next entry, and reuses the space
if their is enough, also allocates space via new char[sz].

@item int present = a.contains(void* ptr)
returns true if ptr is held in one of the ring entries.

@item a.clear()
deletes all space pointed to in any entry. This is called
automatically upon destruction.

@item a.free(void* ptr)
If ptr is one of the entries, calls delete of the pointer,
and resets to entry pointer to null.

@end table

@node String, Integer, AllocRing, Top
@chapter The String class

The @code{String} class is designed to extend GNU C++ to support
string processing capabilities similar to those in languages like
Awk.  The class provides facilities that ought to be convenient
and efficient enough to be useful replacements for @code{char*}
based processing via the C string library (i.e., @code{strcpy,
strcmp,} etc.) in many applications. Many details about String
representations are described in the Representation section.

A separate @code{SubString} class supports substring extraction
and modification operations. This is implemented in a way that
user programs never directly construct or represent substrings,
which are only used indirectly via String operations.

Another separate class, @code{Regex} is also used indirectly via String
operations in support of regular expression searching, matching, and the
like.  The Regex class is based entirely on the GNU Emacs regex
functions.  @xref{Regexps, Syntax of Regular Expressions, Syntax of
Regular Expressions, emacs.info, GNU Emacs Manual}, for a full
explanation of regular expression syntax.  (For implementation details,
see the internal documentation in files @file{regex.h} and
@file{regex.c}.)

@section  Constructors

Strings are initialized and assigned as in the following examples:

@table @code

@item String x;  String y = 0; String z = "";
Set x, y, and z to the nil string. Note that either 0 or "" may 
always be used to refer to the nil string.

@item String x = "Hello"; String y("Hello");
Set x and y to a copy of the string "Hello".

@item String x = 'A'; String y('A');
Set x and y to the string value "A"

@item String u = x; String v(x);
Set u and v to the same string as String x

@item String u = x.at(1,4); String v(x.at(1,4));
Set u and v to the length 4 substring of x starting at position 1
(counting indexes from 0).

@item String x("abc", 2); 
Sets x to "ab", i.e., the first 2 characters of "abc".

@item String x = dec(20);
Sets x to "20". As here, Strings may be initialized or assigned
the results of any @code{char*} function.

@end table

There are no directly accessible forms for declaring SubString
variables.

The declaration @code{Regex r("[a-zA-Z_][a-zA-Z0-9_]*");} creates
a compiled regular expression suitable for use in String
operations described below. (In this case, one that matches any
C++ identifier). The first argument may also be a String.
Be careful in distinguishing the role of backslashes in quoted
GNU C++ char* constants versus those in Regexes. For example, a Regex
that matches either one or more tabs or all strings beginning
with "ba" and ending with any number of occurrences of "na"
could be declared as @code{Regex r = "\\(\t+\\)\\|\\(ba\\(na\\)*\\)"}
Note that only one backslash is needed to signify the tab, but
two are needed for the parenthesization and virgule, since the
GNU C++ lexical analyzer decodes and strips backslashes before
they are seen by Regex.

There are three additional optional arguments to the Regex constructor 
that are less commonly useful:

@table @code
@item fast (default 0)
@code{fast} may be set to true (1) if the Regex should be
"fast-compiled". This causes an additional compilation step that
is generally worthwhile if the Regex will be used many times.

@item bufsize (default max(40, length of the string))
This is an estimate of the size of the internal compiled
expression. Set it to a larger value if you know that the
expression will require a lot of space. If you do not know, 
do not worry: realloc is used if necessary.

@item transtable (default none == 0)
The address of a byte translation table (a char[256]) that
translates each character before matching.

@end table

As a convenience, several Regexes are predefined and usable in
any program. Here are their declarations from @file{String.h}.

@smallexample
extern Regex RXwhite;      // = "[ \n\t]+"
extern Regex RXint;        // = "-?[0-9]+"
extern Regex RXdouble;     // = "-?\\(\\([0-9]+\\.[0-9]*\\)\\|
                           //    \\([0-9]+\\)\\|
                           //    \\(\\.[0-9]+\\)\\)
                           //    \\([eE][---+]?[0-9]+\\)?"
extern Regex RXalpha;      // = "[A-Za-z]+"
extern Regex RXlowercase;  // = "[a-z]+"
extern Regex RXuppercase;  // = "[A-Z]+"
extern Regex RXalphanum;   // = "[0-9A-Za-z]+"
extern Regex RXidentifier; // = "[A-Za-z_][A-Za-z0-9_]*"

@end smallexample

@section Examples

Most @code{String} class capabilities are best shown via example.
The examples below use the following declarations.

@example
    String x = "Hello";
    String y = "world";
    String n = "123";
    String z;
    char*  s = ",";
    String lft, mid, rgt;
    Regex  r = "e[a-z]*o";
    Regex  r2("/[a-z]*/");
    char   c;
    int    i, pos, len;
    double f;
    String words[10];
    words[0] = "a";
    words[1] = "b";
    words[2] = "c";
    
@end example

@section Comparing, Searching and Matching

The usual lexicographic relational operators (@code{==, !=, <, <=, >, >=}) 
are defined. A functional form @code{compare(String, String)} is also
provided, as is @code{fcompare(String, String)}, which compares
Strings without regard for upper vs. lower case.

All other matching and searching operations are based on some form of the
(non-public) @code{match} and @code{search} functions.  @code{match} and
@code{search} differ in that @code{match} attempts to match only at the
given starting position, while @code{search} starts at the position, and
then proceeds left or right looking for a match.  As seen in the following
examples, the second optional @code{startpos} argument to functions using
@code{match} and @code{search} specifies the starting position of the
search: If non-negative, it results in a left-to-right search starting at
position @code{startpos}, and if negative, a right-to-left search starting
at position @code{x.length() + startpos}. In all cases, the index returned
is that of the beginning of the match, or -1 if there is no match. 

Three String functions serve as front ends to @code{search} and @code{match}.
@code{index} performs a search, returning the index, @code{matches} performs
a match, returning nonzero (actually, the length of the match) on success,
and @code{contains} is a boolean function performing either a search or
match, depending on whether an index argument is provided:

@table @code

@item x.index("lo")
returns the zero-based index of the leftmost occurrence of
substring "lo" (3, in this case).  The argument may be a 
String, SubString, char, char*, or Regex.

@item x.index("l", 2)
returns the index of the first of the leftmost occurrence of "l"
found starting the search at position x[2], or 2 in this case.

@item x.index("l", -1)
returns the index of the rightmost occurrence of "l", or 3 here.

@item x.index("l", -3)
returns the index of the rightmost occurrence of "l" found by
starting the search at the 3rd to the last position of x,
returning 2 in this case.

@item pos = r.search("leo", 3, len, 0)
returns the index of r in the @code{char*} string of length 3,
starting at position 0, also placing the  length of the match
in reference parameter len.

@item x.contains("He")
returns nonzero if the String x contains the substring "He". The
argument may be a String, SubString, char, char*, or Regex.

@item x.contains("el", 1)
returns nonzero if x contains the substring "el" at position 1.
As in this example, the second argument to @code{contains},
if present, means to match the substring only at that position,
and not to search elsewhere in the string.

@item x.contains(RXwhite);
returns nonzero if x contains any whitespace (space, tab, or
newline). Recall that @code{RXwhite} is a global whitespace Regex.

@item x.matches("lo", 3)
returns nonzero if x starting at position 3 exactly matches "lo", with
no trailing characters (as it does in this example).

@item x.matches(r)
returns nonzero if String x as a whole matches Regex r.

@item int f = x.freq("l")
returns the number of distinct, nonoverlapping matches to the argument
(2 in this case).

@end table

@section Substring extraction

Substrings may be extracted via the @code{at}, @code{before},
@code{through}, @code{from}, and @code{after} functions.  
These behave as either lvalues or rvalues.

@table @code

@item z = x.at(2, 3)
sets String z to be equal to the length 3 substring of String x
starting at zero-based position 2, setting z to "llo" in this
case. A nil String is returned if the arguments don't make sense.

@item x.at(2, 2) = "r"
Sets what was in positions 2 to 3 of x to "r", setting x to
"Hero" in this case. As indicated here, SubString assignments may
be of different lengths.

@item x.at("He") = "je";
x("He") is the substring of x that matches the first occurrence of
it's argument. The substitution sets x to "jello". If "He" did
not occur, the substring would be nil, and the assignment would
have no effect.

@item  x.at("l", -1) = "i";
replaces the rightmost occurrence of "l" with "i", setting x to
"Helio".

@item z = x.at(r)
sets String z to the first match in x of Regex r, or "ello" in this
case. A nil String is returned if there is no match.

@item z = x.before("o")
sets z to the part of x to the left of the first occurrence of
"o", or "Hell" in this case. The argument may also be a String,
SubString, or Regex.  (If there is no match, z is set to "".)

@item x.before("ll") = "Bri";
sets the part of x to the left of "ll" to "Bri", setting x to
"Brillo".

@item z = x.before(2)
sets z to the part of x to the left of x[2], or "He" in this
case.

@item z = x.after("Hel")
sets z to the part of x to the right of "Hel", or "lo" in this
case.

@item z = x.through("el")
sets z to the part of x up and including "el", or "Hel" in this case.

@item z = x.from("el")
sets z to the part of x from "el" to the end, or "ello" in this case.

@item x.after("Hel") = "p";  
sets x to "Help";

@item z = x.after(3)
sets z to the part of x to the right of x[3] or "o" in this case.

@item z = "  ab c"; z = z.after(RXwhite)  
sets z to the part of its old string to the right of the first
group of whitespace, setting z to "ab c"; Use gsub(below) to
strip out multiple occurrences of whitespace or any pattern.

@item x[0] = 'J';
sets the first element of x to 'J'. x[i] returns a reference to
the ith element of x, or triggers an error if i is out of range. 

@item common_prefix(x, "Help")
returns the String containing the common prefix of the two Strings
or "Hel" in this case.

@item common_suffix(x, "to")
returns the String containing the common suffix of the two Strings
or "o" in this case.

@end table

@section Concatenation

@table @code

@item  z = x + s + ' ' + y.at("w") + y.after("w") + ".";
sets z to "Hello, world."

@item x += y;
sets x to "Helloworld"

@item cat(x, y, z)
A faster way to say z = x + y.

@item cat(z, y, x, x)
Double concatenation; A faster way to say x = z + y + x.

@item y.prepend(x);
A faster way to say y = x + y.

@item z = replicate(x, 3);
sets z to "HelloHelloHello".

@item z = join(words, 3, "/")
sets z to the concatenation of the first 3 Strings in String
array words, each separated by "/", setting z to "a/b/c" in this
case.  The last argument may be "" or 0, indicating no separation.

@end table

@section Other manipulations

@table @code

@item z = "this string has five words"; i = split(z, words, 10, RXwhite);
sets up to 10 elements of String array words to the parts of z
separated by whitespace, and returns the number of parts actually
encountered (5 in this case). Here, words[0] = "this", words[1] =
"string", etc.  The last argument may be any of the usual.
If there is no match, all of z ends up in words[0]. The words array
is @emph{not} dynamically created by split. 

@item int nmatches x.gsub("l","ll")
substitutes all original occurrences of "l" with "ll", setting x
to "Hellllo". The first argument may be any of the usual,
including Regex.  If the second argument is "" or 0, all
occurrences are deleted. gsub returns the number of matches
that were replaced.

@item z = x + y;  z.del("loworl");
deletes the leftmost occurrence of "loworl" in z, setting z to
"Held".

@item z = reverse(x)
sets z to the reverse of x, or "olleH".

@item z = upcase(x)
sets z to x, with all letters set to uppercase, setting z to "HELLO"

@item z = downcase(x)
sets z to x, with all letters set to lowercase, setting z to "hello"

@item z = capitalize(x)
sets z to x, with the first letter of each word set to uppercase, 
and all others to lowercase, setting z to "Hello"

@item x.reverse(), x.upcase(), x.downcase(), x.capitalize()
in-place, self-modifying versions of the above.

@end table

@section Reading, Writing and Conversion

@table @code

@item cout << x 
writes out x. 

@item cout << x.at(2, 3)
writes out the substring "llo".

@item cin >> x
reads a whitespace-bounded string into x.

@item x.length()
returns the length of String x (5, in this case).

@item s = (const char*)x
can be used to extract the @code{char*} char array. This
coercion is useful for sending a String as an argument to any
function expecting a @code{const char*} argument (like
@code{atoi}, and @code{File::open}). This operator must be
used with care, since the conversion returns a pointer
to @code{String} internals without copying the characters:
The resulting @code{(char*)} is only valid until
the next String operation,  and you must not modify it.
(The conversion is defined to return a const
value so that GNU C++ will produce warning and/or error
messages if changes are attempted.)

@end table

@node Integer, Rational, String, Top
@chapter The Integer class.

The @code{Integer} class provides multiple precision integer arithmetic
facilities. Some representation details are discussed in the 
Representation section.

@code{Integers} may be up to @code{b * ((1 << b) - 1)} bits long, where
@code{b} is the number of bits per short (typically 1048560 bits when
@code{b = 16}).  The implementation assumes that a @code{long} is at least
twice as long as a @code{short}. This assumption hides beneath almost all
primitive operations, and would be very difficult to change. It also relies
on correct behavior of @emph{unsigned} arithmetic operations.

Some of the arithmetic algorithms are very loosely based on those
provided in the MIT Scheme @file{bignum.c} release, which is
Copyright (c) 1987 Massachusetts Institute of Technology. Their use
here falls within the provisions described in the Scheme release.

Integers may be constructed in the following ways:
@table @code

@item Integer x;
Declares an uninitialized Integer.

@item Integer x = 2; Integer y(2);
Set x and y to the Integer value 2;

@item Integer u(x); Integer v = x;
Set u and v to the same value as x.

@end table

@deftypefn Method long Integer::as_long() const
Used to coerce an @code{Integer} back into longs via the @code{long}
coercion operator. If the Integer cannot fit into a long, this returns
MINLONG or MAXLONG (depending on the sign) where MINLONG is the most
negative, and MAXLONG is the most positive representable long.
@end deftypefn

@deftypefn Method int Integer::fits_in_long() const
Returns true iff the @code{Integer} is @code{< MAXLONG} and @code{> MINLONG}.
@end deftypefn

@deftypefn Method double Integer::as_double() const
Coerce the @code{Integer} to a @code{double}, with potential
loss of precision.
@code{+/-HUGE} is returned if the Integer cannot fit into a double.
@end deftypefn

@deftypefn Method int Integer::fits_in_double() const
Returns true iff the @code{Integer} can fit into a double.
@end deftypefn

All of the usual arithmetic operators are provided (@code{+, -, *, /,
%, +=, ++, -=, --, *=, /=, %=, ==, !=, <, <=, >, >=}).  All operators
support special versions for mixed arguments of Integers and regular
C++ longs in order to avoid useless coercions, as well as to allow
automatic promotion of shorts and ints to longs, so that they may be
applied without additional Integer coercion operators.  The only
operators that behave differently than the corresponding int or long
operators are @code{++} and @code{--}.  Because C++ does not
distinguish prefix from postfix application, these are declared as
@code{void} operators, so that no confusion can result from applying
them as postfix.  Thus, for Integers x and y, @code{ ++x; y = x; } is
correct, but @code{ y = ++x; } and @code{ y = x++; } are not.

Bitwise operators (@code{~}, @code{&}, @code{|}, @code{^}, @code{<<}, 
@code{>>}, @code{&=}, @code{|=}, @code{^=}, @code{<<=}, @code{>>=}) are
also provided.  However, these operate on sign-magnitude, rather than
two's complement representations. The sign of the result is arbitrarily
taken as the sign of the first argument. For example, @code{Integer(-3)
& Integer(5)} returns @code{Integer(-1)}, not -3, as it would using
two's complement. Also, @code{~}, the complement operator, complements
only those bits needed for the representation.  Bit operators are also
provided in the BitSet and BitString classes. One of these classes
should be used instead of Integers when the results of bit manipulations
are not interpreted numerically.

The following utility functions are also provided. (All arguments
are Integers unless otherwise noted).

@deftypefun void divide(const Integer& @var{x}, const Integer& @var{y}, Integer& @var{q}, Integer& @var{r})
Sets @var{q} to the quotient and @var{r} to the remainder of @var{x} and @var{y}.
(@var{q} and @var{r} are returned by reference). 
@end deftypefun

@deftypefun Integer pow(const Integer& @var{x}, const Integer& @var{p})
Returns @var{x} raised to the power @var{p}.
@end deftypefun

@deftypefun Integer Ipow(long @var{x}, long @var{p})
Returns @var{x} raised to the power @var{p}.
@end deftypefun

@deftypefun Integer gcd(const Integer& @var{x}, const Integer& @var{p})
Returns the greatest common divisor of @var{x} and @var{y}.
@end deftypefun

@deftypefun Integer lcm(const Integer& @var{x}, const Integer& @var{p})
Returns the least common multiple of @var{x} and @var{y}.
@end deftypefun

@deftypefun Integer abs(const Integer& @var{x}
Returns the absolute value of @var{x}.
@end deftypefun

@deftypefn Method void Integer::negate()
Negates @code{this} in place.
@end deftypefn

@table @code

@item Integer sqr(x)
returns x * x;

@item Integer sqrt(x)
returns the floor of the  square root of x.

@item long lg(x);
returns the floor of the base 2 logarithm of abs(x)

@item int sign(x)
returns -1 if x is negative, 0 if zero, else +1.
Using @code{if (sign(x) == 0)} is a generally faster method
of testing for zero than using relational operators.

@item int even(x)
returns true if x is an even number

@item int odd(x)
returns true if x is an odd number.

@item void setbit(Integer& x, long b)
sets the b'th bit (counting right-to-left from zero) of x to 1.

@item void clearbit(Integer& x, long b)
sets the b'th bit of x to 0.

@item int testbit(Integer x, long b)
returns true if the b'th bit of x is 1.

@item Integer atoI(char* asciinumber, int base = 10);
converts the base base char* string into its Integer form.

@item void Integer::printon(ostream& s, int base = 10, int width = 0);
prints the ascii string value of @code{(*this)} as a base @code{base}
number, in field width at least @code{width}.

@item ostream << x;
prints x in base ten format.

@item istream >> x;
reads x as a base ten number.

@item int compare(Integer x, Integer y)
returns a negative number if x<y, zero if x==y, or positive if x>y.

@item int ucompare(Integer x, Integer y)
like compare, but performs unsigned comparison.

@item add(x, y, z)
A faster way to say z = x + y.

@item sub(x, y, z)
A faster way to say z = x - y.

@item mul(x, y, z)
A faster way to say z = x * y.

@item div(x, y, z)
A faster way to say z = x / y.

@item mod(x, y, z)
A faster way to say z = x % y.

@item and(x, y, z)
A faster way to say z = x & y.

@item or(x, y, z)
A faster way to say z = x | y.

@item xor(x, y, z)
A faster way to say z = x ^ y.

@item lshift(x, y, z)
A faster way to say z = x << y.

@item rshift(x, y, z)
A faster way to say z = x >> y.

@item pow(x, y, z)
A faster way to say z = pow(x, y).

@item complement(x, z)
A faster way to say z = ~x.

@item negate(x, z)
A faster way to say z = -x.

@end table

@node Rational, Complex, Integer, Top
@chapter The Rational Class

Class @code{Rational} provides multiple precision rational
number arithmetic. All rationals are maintained in simplest
form (i.e., with the numerator and denominator relatively
prime, and with the denominator strictly positive).
Rational arithmetic and relational operators are provided 
(@code{+, -, *, /, +=, -=, *=, /=, ==, !=, <, <=, >, >=}). 
Operations resulting in a rational number with zero denominator 
trigger an exception.

Rationals may be constructed and used in the following ways:

@table @code

@item Rational x;
Declares an uninitialized Rational.

@item Rational x = 2; Rational y(2);
Set x and y to the Rational value 2/1;

@item Rational x(2, 3);
Sets x to the Rational value 2/3;

@item Rational x = 1.2;
Sets x to a Rational value close to 1.2. Any double precision value
may be used to construct a Rational. The Rational will possess
exactly as much precision as the double. Double values that do
not have precise floating point equivalents (like 1.2) produce
similarly imprecise rational values. 

@item Rational x(Integer(123), Integer(4567));
Sets x to the Rational value 123/4567.

@item Rational u(x); Rational v = x;
Set u and v to the same value as x.

@item double(Rational x)
A Rational may be coerced to a double with potential 
loss of precision. +/-HUGE is returned if it will not fit.

@item Rational abs(x)
returns the absolute value of x.

@item void x.negate()
negates x.

@item void x.invert()
sets x to 1/x.

@item int sign(x)
returns 0 if x is zero, 1 if positive, and -1 if negative.

@item Rational sqr(x)
returns x * x.

@item Rational pow(x, Integer y)
returns x to the y power.

@item Integer x.numerator()
returns the numerator.

@item Integer x.denominator()
returns the denominator.

@item Integer floor(x)
returns the greatest Integer less than x.

@item Integer ceil(x)
returns the least Integer greater than x.

@item Integer trunc(x)
returns the Integer part of x.

@item Integer round(x)
returns the nearest Integer to x.

@item int compare(x, y)
returns a negative, zero, or positive number signifying whether x is
less than, equal to, or greater than y.

@item ostream << x;
prints x in the form num/den, or just num if the denominator is one.

@item istream >> x;
reads x in the form num/den, or just num in which case the 
denominator is set to one.

@item add(x, y, z)
A faster way to say z = x + y.

@item sub(x, y, z)
A faster way to say z = x - y.

@item mul(x, y, z)
A faster way to say z = x * y.

@item div(x, y, z)
A faster way to say z = x / y.

@item pow(x, y, z)
A faster way to say z = pow(x, y).

@item negate(x, z)
A faster way to say z = -x.

@end table

@node Complex, Fix, Rational, Top
@chapter The Complex class.

Class @code{Complex} is implemented in a way similar to that
described by Stroustrup. In keeping with libg++ conventions,
the class is named @code{Complex}, not @code{complex}.
Complex arithmetic and relational operators are provided 
(@code{+, -, *, /, +=, -=, *=, /=, ==, !=}). 
Attempted division by (0, 0) triggers an exception.

Complex numbers may be constructed and used in the following ways:

@table @code

@item Complex x;
Declares an uninitialized Complex.

@item Complex x = 2; Complex y(2.0);
Set x and y to the Complex value (2.0, 0.0);

@item Complex x(2, 3);
Sets x to the Complex value (2, 3);

@item Complex u(x); Complex v = x;
Set u and v to the same value as x.

@item double real(Complex& x);
returns the real part of x.

@item double imag(Complex& x);
returns the imaginary part of x.

@item double abs(Complex& x);
returns the magnitude of x.

@item double norm(Complex& x);
returns the square of the magnitude of x.

@item double arg(Complex& x);
returns the argument (amplitude) of x.

@item Complex polar(double r, double t = 0.0);
returns a Complex with abs of r and arg of t.

@item Complex conj(Complex& x);
returns the complex conjugate of x.

@item Complex cos(Complex& x);
returns the complex cosine of x.

@item Complex sin(Complex& x);
returns the complex sine of x.

@item Complex cosh(Complex& x);
returns the complex hyperbolic cosine of x.

@item Complex sinh(Complex& x);
returns the complex hyperbolic sine of x.

@item Complex exp(Complex& x);
returns the exponential of x.

@item Complex log(Complex& x);
returns the natural log of x.

@item Complex pow(Complex& x, long p);
returns x raised to the p power.

@item Complex pow(Complex& x, Complex& p);
returns x raised to the p power.

@item Complex sqrt(Complex& x);
returns the square root of x.

@item ostream << x;
prints x in the form (re, im).

@item istream >> x;
reads x in the form (re, im), or just (re) or re in which case the 
imaginary part is set to zero.

@end table

@node Fix, Bit, Complex, Top
@chapter  Fixed precision numbers

Classes @code{Fix16}, @code{Fix24}, @code{Fix32}, and @code{Fix48}
support operations on 16, 24, 32, or 48 bit quantities that are
considered as real numbers in the range [-1, +1).  Such numbers are
often encountered in digital signal processing applications. The classes
may be be used in isolation or together.  Class @code{Fix32}
operations are entirely self-contained.  Class @code{Fix16} operations
are self-contained except that the multiplication operation @code{Fix16
* Fix16} returns a @code{Fix32}. @code{Fix24} and @code{Fix48} are
similarly related.

The standard arithmetic and relational operations are supported
(@code{=}, @code{+}, @code{-}, @code{*}, @code{/}, @code{<<}, @code{>>},
@code{+=}, @code{-=}, @code{*=}, @code{/=}, @code{<<=}, @code{>>=},
@code{==}, @code{!=}, @code{<}, @code{<=}, @code{>}, @code{>=}).
All operations include provisions for special handling in cases where
the result exceeds +/- 1.0. There are two cases that may be handled
separately: ``overflow'' where the results of addition and subtraction
operations go out of range, and all other ``range errors'' in which
resulting values go off-scale (as with division operations, and
assignment or initialization with off-scale values). In signal
processing applications, it is often useful to handle these two cases
differently. Handlers take one argument, a reference to the integer
mantissa of the offending value, which may then be manipulated.  In
cases of overflow, this value is the result of the (integer) arithmetic
computation on the mantissa; in others it is a fully saturated (i.e.,
most positive or most negative) value. Handling may be reset to any of
several provided functions or any other user-defined function via
@code{set_overflow_handler} and @code{set_range_error_handler}. The
provided functions for @code{Fix16} are as follows (corresponding
functions are also supported for the others).

@table @code

@item Fix16_overflow_saturate
The default overflow handler. Results are ``saturated'': positive results
are set to the largest representable value (binary 0.111111...), and
negative values to -1.0.

@item Fix16_ignore
Performs no action. For overflow, this will allow addition and
subtraction operations to ``wrap around'' in the same manner
as integer arithmetic, and for saturation, will leave values saturated.

@item Fix16_overflow_warning_saturate
Prints a warning message on standard error, then saturates the results.

@item Fix16_warning
The default range_error handler. Prints a warning message
on standard error; otherwise leaving the argument unmodified.

@item Fix16_abort
prints an error message on standard error, then aborts execution. 


@end table

In addition to arithmetic operations, the following are provided:

@table @code

@item Fix16 a = 0.5; 
Constructs fixed precision objects from double precision values.
Attempting to initialize to a value outside the range invokes
the range_error handler, except, as a convenience, 
initialization to 1.0 sets the variable to the most positive 
representable value (binary 0.1111111...) without invoking the handler.

@item short& mantissa(a); long& mantissa(b);
return a * pow(2, 15) or b * pow(2, 31) as an integer. These
are returned by reference, to enable ``manual'' data manipulation.

@item double value(a); double value(b);
return a or b as floating point numbers.

@end table

@node Bit, Random, Fix, Top
@chapter  Classes for Bit manipulation

libg++ provides several different classes supporting the use
and manipulation of collections of bits in different ways.

@itemize @bullet

@item
Class @code{Integer} provides ``integer'' semantics. It supports
manipulation of bits in ways that are often useful when treating bit arrays
as numerical (integer) quantities.  This class is described elsewhere.

@item 
Class @code{BitSet} provides ``set'' semantics. It supports operations
useful when treating collections of bits as representing potentially
infinite sets of integers.

@item
Class @code{BitSet32} supports fixed-length BitSets holding exactly
32 bits.

@item
Class @code{BitSet256} supports fixed-length BitSets holding exactly
256 bits.

@item
Class @code{BitString} provides ``string'' (or ``vector'') semantics. 
It supports operations useful when treating collections of bits as 
strings of zeros and ones.

@end itemize

These classes also differ in the following ways:

@itemize @bullet


@item
BitSets are logically infinite. Their space is dynamically altered to
adjust to the smallest number of consecutive bits actually required to
represent the sets. Integers also have this property. BitStrings are
logically finite, but their sizes are internally dynamically managed to
maintain proper length. This means that, for example, BitStrings are
concatenatable while BitSets and Integers are not. 

@item
BitSet32 and BitSet256 have precisely the same properties as BitSets,
except that they use constant fixed length bit vectors.

@item
While all classes support basic unary and binary operations @code{~, &,
|, ^, -}, the semantics differ. BitSets perform bit operations that
precisely mirror those for infinite sets. For example, complementing an
empty BitSet returns one representing an infinite number of set bits.
Operations on BitStrings and Integers operate only on those bits
actually present in the representation.  For BitStrings and Integers,
the the @code{&} operation returns a BitString with a length equal to
the minimum length of the operands, and @code{|, ^} return one with
length of the maximum.

@item
Only BitStrings support substring extraction and bit pattern matching.

@end itemize

@section BitSet

BitSets are objects that contain logically infinite sets of nonnegative
integers.  Representational details are discussed in the Representation
chapter. Because they are logically infinite, all BitSets possess a
trailing, infinitely replicated 0 or 1 bit, called the ``virtual bit'', and
indicated via 0* or 1*.

BitSet32 and BitSet256 have they same properties, except they are
of fixed length, and thus have no virtual bit. 

BitSets may be constructed as follows:

@table @code

@item BitSet a;
declares an empty BitSet.

@item BitSet a = atoBitSet("001000");
sets a to the BitSet 0010*, reading left-to-right. The ``0*''
indicates that the set ends with an infinite number of zero
(clear) bits.

@item BitSet a = atoBitSet("00101*");
sets a to the BitSet 00101*, where ``1*'' means that the set ends
with an infinite number of one (set) bits.

@item BitSet a = longtoBitSet((long)23);
sets a to the BitSet 111010*, the binary representation of decimal 23.

@item BitSet a = utoBitSet((unsigned)23);
sets a to the BitSet 111010*, the binary representation of decimal 23.

@end table

The following functions and operators are provided (Assume the
declaration of BitSets a = 0011010*, b = 101101*, throughout, as
examples).

@table @code

@item ~a
returns the complement of a, or 1100101* in this case.

@item a.complement()
sets a to ~a.

@item a & b; a &= b;
returns a intersected with b, or 0011010*.

@item a | b; a |= b;
returns a unioned with b, or 1011111*.

@item a - b; a -= b;
returns the set difference of a and b, or 000010*.

@item a ^ b; a ^= b;
returns the symmetric difference of a and b, or 1000101*.

@item a.empty()
returns true if a is an empty set.

@item a == b; 
returns true if a and b contain the same set.

@item a <= b;
returns true if a is a subset of b.

@item a < b;
returns true if a is a proper subset of b;

@item a != b; a >= b; a > b;
are the converses of the above.

@item a.set(7)
sets the 7th (counting from 0) bit of a, setting a to 001111010*

@item a.clear(2)
clears the 2nd bit bit of a, setting a to 00011110*

@item a.clear()
clears all bits of a;

@item a.set()
sets all bits of a;

@item a.invert(0)
complements the 0th bit of a, setting a to 10011110*

@item a.set(0,1)
sets the 0th through 1st bits of a, setting a to 110111110*
The two-argument versions of clear and invert are similar.

@item a.test(3)
returns true if the 3rd bit of a is set.

@item a.test(3, 5)
returns true if any of bits 3 through 5 are set.

@item int i = a[3]; a[3] = 0;
The subscript operator allows bits to be inspected and changed
via standard subscript semantics, using a friend class BitSetBit.
The use of the subscript operator a[i] rather than a.test(i) 
requires somewhat greater overhead.

@item a.first(1) or a.first()
returns the index of the first set bit of a (2 in this case), 
or -1 if no bits are set.

@item a.first(0)
returns the index of the first clear bit of a (0 in this case), 
or -1 if no bits are clear.

@item a.next(2, 1) or a.next(2)
returns the index of the next bit after position 2 that is set (3
in this case) or -1. @code{first} and @code{next} may be used as
iterators, as in 
@code{for (int i = a.first(); i >= 0; i = a.next(i))...}.

@item a.last(1)
returns the index of the rightmost set bit, or -1 if there or no set
bits or all set bits.

@item a.prev(3, 0)
returns the index of the previous clear bit before position 3.

@item a.count(1)
returns the number of set bits in a, or -1 if there are 
an infinite number.

@item a.virtual_bit()
returns the trailing (infinitely replicated) bit of a.

@item a = atoBitSet("ababX", 'a', 'b', 'X');
converts the char* string into a bitset, with 'a' denoting false,
'b' denoting true, and 'X' denoting infinite replication.

@item a.printon(cout, '-', '.', 0)
prints @code{a} to @code{cout} represented with
@code{'-'} for falses, @code{'.'} for trues, and no replication marker.

@item cout << a
prints @code{a} to @code{cout} (representing lases by @code{'f'},
trues by @code{'t'}, and using @code{'*'} as the replication marker).

@item diff(x, y, z)
A faster way to say z = x - y.

@item and(x, y, z)
A faster way to say z = x & y.

@item or(x, y, z)
A faster way to say z = x | y.

@item xor(x, y, z)
A faster way to say z = x ^ y.

@item complement(x, z)
A faster way to say z = ~x.

@end table

@section BitString

BitStrings are objects that contain arbitrary-length strings of
zeroes and ones. BitStrings possess some features that make them
behave like sets, and others that behave as strings. They are
useful in applications (such as signature-based algorithms) where
both capabilities are needed.  Representational details are
discussed in the Representation chapter.  Most capabilities are
exact analogs of those supported in the BitSet and String
classes.  A BitSubString is used with substring operations along
the same lines as the String SubString class.  A BitPattern class
is used for masked bit pattern searching.

Only a default constructor is supported.  The declaration
@code{BitString a;} initializes a to be an empty BitString.
BitStrings may often be initialized via @code{atoBitString}
and @code{longtoBitString}.

Set operations (@code{ ~, complement, &, &=, |, |=, -, ^, ^=})
behave just as the BitSet versions, except that there is no
``virtual bit'': complementing complements only those bits in the
BitString, and all binary operations across unequal length
BitStrings assume a virtual bit of zero. The @code{&} operation
returns a BitString with a length equal to the minimum length of
the operands, and @code{|, ^} return one with length of the
maximum.

Set-based relational operations (@code{==, !=, <=, <, >=, >})
follow the same rules. A string-like lexicographic comparison
function, @code{lcompare}, tests the lexicographic relation between
two BitStrings. For example, lcompare(1100, 0101) returns 1,
since the first BitString starts with 1 and the second with 0.

Individual bit setting, testing, and iterator operations 
(@code{set, clear, invert, test, first, next, last, prev})
are also like those for BitSets. BitStrings are automatically
expanded when setting bits at positions greater than their
current length.

The string-based capabilities are just as those for class String.
BitStrings may be concatenated (@code{+, +=}), searched
(@code{index, contains, matches}), and extracted into
BitSubStrings (@code{before, at, after}) which may be assigned and
otherwise manipulated. Other string-based utility functions
(@code{reverse, common_prefix, common_suffix}) are also provided.
These have the same capabilities and descriptions as those
for Strings.

String-oriented operations can also be performed with a mask via
class BitPattern. BitPatterns consist of two BitStrings, a
pattern and a mask. On searching and matching, bits in the pattern
that correspond to 0 bits in the mask are ignored. (The mask may
be shorter than the pattern, in which case trailing mask bits are
assumed to be 0). The pattern and mask are both public variables,
and may be individually subjected to other bit operations.

Converting to char* and printing (@code{(atoBitString,
atoBitPattern, printon, ostream <<)}) are also as in BitSets, 
except that no virtual bit is used, and an 'X' in a BitPattern means
that the pattern bit is masked out.

The following features are unique to BitStrings. 

Assume declarations of BitString a = atoBitString("01010110") and b =
atoBitSTring("1101").

@table @code

@item a = b + c;
Sets a to the concatenation of b and c;

@item a = b + 0; a = b + 1;
sets a to b, appended with a zero (one).

@item a += b;
appends b to a;

@item a += 0; a += 1;
appends a zero (one) to a.

@item a << 2; a <<= 2
return a with 2 zeros prepended, setting a to 0001010110. (Note
the necessary confusion of << and >> operators. For consistency
with the integer versions, << shifts low bits to high, even though
they are printed low bits first.)

@item a >> 3; a >>= 3
return a with the first 3 bits deleted, setting a to 10110.

@item a.left_trim(0)
deletes all 0 bits on the left of a, setting a to 1010110.

@item a.right_trim(0)
deletes all trailing 0 bits of a, setting a to 0101011.

@item cat(x, y, z)
A faster way to say z = x + y.

@item diff(x, y, z)
A faster way to say z = x - y.

@item and(x, y, z)
A faster way to say z = x & y.

@item or(x, y, z)
A faster way to say z = x | y.

@item xor(x, y, z)
A faster way to say z = x ^ y.

@item lshift(x, y, z)
A faster way to say z = x << y.

@item rshift(x, y, z)
A faster way to say z = x >> y.

@item complement(x, z)
A faster way to say z = ~x.

@end table


@node Random, Data, Bit, Top
@chapter Random Number Generators and related classes

The two classes @code{RNG} and @code{Random} are used together to
generate a variety of random number distributions.  A distinction must
be made between @emph{random number generators}, implemented by class
@code{RNG}, and @emph{random number distributions}.  A random number
generator produces a series of randomly ordered bits.  These bits can be
used directly, or cast to other representations, such as a floating
point value.  A random number generator should produce a @emph{uniform}
distribution.  A random number distribution, on the other hand, uses the
randomly generated bits of a generator to produce numbers from a
distribution with specific properties.  Each instance of @code{Random}
uses an instance of class @code{RNG} to provide the raw, uniform
distribution used to produce the specific distribution.  Several
instances of @code{Random} classes can share the same instance of
@code{RNG}, or each instance can use its own copy.

@section RNG

Random distributions are constructed from members of class @code{RNG},
the actual random number generators.  The @code{RNG} class contains no
data; it only serves to define the interface to random number
generators.  The @code{RNG::asLong} member returns an unsigned long
(typically 32 bits) of random bits.  Applications that require a number
of random bits can use this directly.  More often, these random bits are
transformed to a uniform random number:

@smallexample
    //
    // Return random bits converted to either a float or a double
    //
    float asFloat();
    double asDouble();
@};
@end smallexample

@noindent
using either @code{asFloat} or @code{asDouble}.  It is intended that
@code{asFloat} and @code{asDouble} return differing precisions;
typically, @code{asDouble} will draw two random longwords and transform
them into a legal @code{double}, while @code{asFloat} will draw a single
longword and transform it into a legal @code{float}.  These members are
used by subclasses of the @code{Random} class to implement a variety of
random number distributions.

@section ACG

Class @code{ACG} is a variant of a Linear Congruential Generator
(Algorithm M) described in Knuth, @emph{Art of Computer Programming, Vol
III}.  This result is permuted with a Fibonacci Additive Congruential
Generator to get good independence between samples.  This is a very high
quality random number generator, although it requires a fair amount of
memory for each instance of the generator.

The @code{ACG::ACG} constructor takes two parameters: the seed and the
size.  The seed is any number to be used as an initial seed. The
performance of the generator depends on having a distribution of bits
through the seed.  If you choose a number in the range of 0 to 31, a
seed with more bits is chosen. Other values are deterministically
modified to give a better distribution of bits.  This provides a good
random number generator while still allowing a sequence to be repeated
given the same initial seed.

The @code{size} parameter determines the size of two tables used in the
generator. The first table is used in the Additive Generator; see the
algorithm in Knuth for more information. In general, this table is
@code{size} longwords long. The default value, used in the algorithm in
Knuth, gives a table of 220 bytes. The table size affects the period of
the generators; smaller values give shorter periods and larger tables
give longer periods. The smallest table size is 7 longwords, and the
longest is 98 longwords. The @code{size} parameter also determines the
size of the table used for the Linear Congruential Generator. This value
is chosen implicitly based on the size of the Additive Congruential
Generator table. It is two powers of two larger than the power of two
that is larger than @code{size}.  For example, if @code{size} is 7, the
ACG table is 7 longwords and the LCG table is 128 longwords. Thus, the
default size (55) requires 55 + 256 longwords, or 1244 bytes. The
largest table requires 2440 bytes and the smallest table requires 100
bytes.  Applications that require a large number of generators or
applications that aren't so fussy about the quality of the generator may
elect to use the @code{MLCG} generator.

@section MLCG

The @code{MLCG} class implements a @emph{Multiplicative Linear
Congruential Generator}. In particular, it is an implementation of the
double MLCG described in @emph{``Efficient and Portable Combined Random
Number Generators''} by Pierre L'Ecuyer, appearing in
@emph{Communications of the ACM, Vol. 31. No. 6}. This generator has a
fairly long period, and has been statistically analyzed to show that it
gives good inter-sample independence.

The @code{MLCG::MLCG} constructor has two parameters, both of which are
seeds for the generator. As in the @code{MLCG} generator, both seeds are
modified to give a ``better'' distribution of seed digits. Thus, you can
safely use values such as `0' or `1' for the seeds. The @code{MLCG}
generator used much less state than the @code{ACG} generator; only two
longwords (8 bytes) are needed for each generator.

@section Random

A random number generator may be declared by first declaring a
@code{RNG} and then a @code{Random}. For example, @code{ACG gen(10, 20);
NegativeExpntl rnd (1.0, &gen);} declares an additive congruential
generator with seed 10 and table size 20, that is used to generate
exponentially distributed values with mean of 1.0.

The virtual member @code{Random::operator()} is the common way of
extracting a random number from a particular distribution.  The base
class, @code{Random} does not implement @code{operator()}. This is
performed by each of the subclasses. Thus, given the above declaration
of @code{rnd}, new random values may be obtained via, for example,
@code{double next_exp_rand = rnd();} Currently, the following subclasses
are provided.

@section Binomial

The binomial distribution models successfully drawing items from
a pool.  The first parameter to the constructor, @code{n}, is the
number of items in the pool, and the second parameter, @code{u},
is the probability of each item being successfully drawn.  The
member @code{asDouble} returns the number of samples drawn from
the pool.  Although it is not checked, it is assumed that
@code{n>0} and @code{0 <= u <= 1}.  The remaining members allow
you to read and set the parameters.

@section Erlang

The @code{Erlang} class implements an Erlang distribution with
mean @code{mean} and variance @code{variance}.

@section Geometric

The @code{Geometric} class implements a discrete geometric
distribution.  The first parameter to the constructor,
@code{mean}, is the mean of the distribution.  Although it is not
checked, it is assumed that @code{0 <= mean <= 1}.
@code{Geometric()} returns the number of uniform random samples
that were drawn before the sample was larger than @code{mean}.
This quantity is always greater than zero.

@section HyperGeometric

The @code{HyperGeometric} class implements the hypergeometric
distribution.  The first parameter to the constructor,
@code{mean}, is the mean and the second, @code{variance}, is the
variance.  The remaining members allow you to inspect and change
the mean and variance.

@section NegativeExpntl

The @code{NegativeExpntl} class implements the negative
exponential distribution.  The first parameter to the constructor
is the mean.  The remaining members allow you to inspect and
change the mean.

@section Normal

The @code{Normal}class implements the normal distribution.  The
first parameter to the constructor, @code{mean}, is the mean and
the second, @code{variance}, is the variance.  The remaining
members allow you to inspect and change the mean and variance.
The @code{LogNormal} class is a subclass of @code{Normal}.

@section LogNormal

The @code{LogNormal}class implements the logarithmic normal
distribution.  The first parameter to the constructor,
@code{mean}, is the mean and the second, @code{variance}, is the
variance.  The remaining members allow you to inspect and change
the mean and variance.  The @code{LogNormal} class is a subclass
of @code{Normal}.

@section Poisson

The @code{Poisson} class implements the poisson distribution.
The first parameter to the constructor is the mean.  The
remaining members allow you to inspect and change the mean.

@section DiscreteUniform

The @code{DiscreteUniform} class implements a uniform random variable over
the closed interval ranging from @code{[low..high]}.  The first parameter
to the constructor is @code{low}, and the second is @code{high}, although
the order of these may be reversed.  The remaining members allow you to
inspect and change @code{low} and @code{high}.

@section Uniform

The @code{Uniform} class implements a uniform random variable over the
open interval ranging from @code{[low..high)}.  The first parameter to
the constructor is @code{low}, and the second is @code{high}, although
the order of these may be reversed.  The remaining members allow you to
inspect and change @code{low} and @code{high}.@refill

@section Weibull

The @code{Weibull} class implements a weibull distribution with
parameters @code{alpha} and @code{beta}.  The first parameter to
the class constructor is @code{alpha}, and the second parameter
is @code{beta}.  The remaining members allow you to inspect and
change @code{alpha} and @code{beta}.

@section RandomInteger

The @code{RandomInteger} class is @emph{not} a subclass of Random,
but a stand-alone integer-oriented class that is dependent on the
RNG classes. RandomInteger returns random integers uniformly from
the closed interval @code{[low..high]}.  The first parameter to the
constructor is @code{low}, and the second is @code{high}, although
both are optional.  The last argument is always a generator.
Additional members allow you to inspect and change @code{low} and
@code{high}.  Random integers are generated using @code{asInt()} or
@code{asLong()}.  Operator syntax (@code{()}) is also available as a
shorthand for @code{asLong()}.  Because @code{RandomInteger} is often
used in simulations for which uniform random integers are desired over
a variety of ranges, @code{asLong()} and @code{asInt} have @code{high}
as an optional argument.  Using this optional argument produces a
single value from the new range, but does not change the default
range.


@node Data, Curses, Random, Top
@chapter Data Collection
Libg++ currently provides two classes for @emph{data collection}
and analysis of the collected data.

@section SampleStatistic

Class @code{SampleStatistic} provides a means of accumulating
samples of @code{double} values and providing common sample statistics.

Assume declaration of @code{double x}.

@table @code 

@item SampleStatistic a;
declares and initializes a.

@item a.reset();
re-initializes a.

@item a += x;
adds sample x.

@item int n = a.samples();
returns the number of samples.

@item x = a.mean;
returns the means of the samples.

@item x = a.var()
returns the sample variance of the samples.

@item x = a.stdDev()
returns the sample standard deviation of the samples.

@item x = a.min()
returns the minimum encountered sample.

@item x = a.max()
returns the maximum encountered sample.

@item x = a.confidence(int p)
returns the p-percent (0 <= p < 100) confidence interval.

@item x = a.confidence(double p)
returns the p-probability (0 <= p < 1) confidence interval.


@end table

@section SampleHistogram

Class @code{SampleHistogram} is a derived class of
@code{SampleStatistic} that supports collection and display of samples
in bucketed intervals. It supports the following in addition to
@code{SampleStatisic} operations.

@table @code

@item SampleHistogram h(double lo, double hi, double width);
declares and initializes h to have buckets of size width from lo to hi.
If the optional argument width is not specified, 10 buckets are
created. The first bucket and also holds samples less than lo,
and the last one holds samples greater than hi.

@item int n = h.similarSamples(x)
returns the number of samples in the same bucket as x.

@item int n = h.inBucket(int i)
returns the number of samples in  bucket i.

@item int b = h.buckets()
returns the number of buckets.

@item h.printBuckets(ostream s)
prints bucket counts on ostream s.

@item double bound = h.bucketThreshold(int i)
returns the upper bound of bucket i.


@end table

@node Curses, List, Data, Top
@chapter Curses-based classes

The @code{CursesWindow} class is a repackaging of standard
curses library features into a class. It relies on @file{curses.h}.

The supplied @file{curses.h} is a fairly conservative declaration
of curses library features, and does not include features like
``screen'' or X-window support. It is, for the most part, an
adaptation, rather than an improvement of C-based @file{curses.h}
files. The only substantive changes are the declarations of
many functions as inline functions rather than macros, which
was done solely to allow overloading.

The @code{CursesWindow} class encapsulates curses window functions
within a class. Only those functions that control windows are included:
Terminal control functions and macros like @code{cbreak} are not part
of the class.  All @code{CursesWindows} member functions have names
identical to the corresponding curses library functions, except that the
``w'' prefix is generally dropped. Descriptions of these functions may
be found in your local curses library documentation.

A @code{CursesWindow} may be declared via

@table @code

@item CursesWindow w(WINDOW* win)
attaches w to the existing WINDOW* win. This is constructor is normally
used only in the following special case.

@item CursesWindow w(stdscr)
attaches w to the default curses library standard screen window.

@item CursesWindow w(int lines, int cols, int begin_y, int begin_x)
attaches to an allocated curses window with the indicated size and
screen position.

@item CursesWindow sub(CursesWindow& w,int l,int c,int by,int bx,char ar='a')
attaches to a subwindow of w created via the curses `subwin' command.
If ar is sent as `r', the origin (by, bx) is relative to the parent 
window, else it is absolute.

@end table

The class maintains a static counter that is used in order to
automatically call the curses library @code{initscr} and @code{endscr}
functions at the proper times. These need not, and should not be
called ``manually''.

@code{CursesWindow}s maintain a tree of their subwindows. Upon
destruction of a @code{CursesWindow}, all of their subwindows are
also invalidated if they had not previously been destroyed.

It is possible to traverse trees of subwindows via the following
member functions

@table @code

@item CursesWindow* w.parent()
returns a pointer to the parent of the subwindow, or 0 if there is none.

@item CursesWindow* w.child()
returns the first child subwindow of the window, or 0 if there is none.

@item CursesWindow* w.sibling()
returns the next sibling of the subwindow, or 0 if there is none.

@end table

For example, to call some function @code{visit} for all subwindows
of a window, you could write

@example

void traverse(CursesWindow& w)
@{
  visit(w);
  if (w.child() != 0) traverse(*w.child);
  if (w.sibling() != 0) traverse(*w.sibling);
@}

@end example
   
@node List, LinkList, Curses, Top
@chapter List classes

The files @file{g++-include/List.hP} and @file{g++-include/List.ccP}
provide pseudo-generic Lisp-type List classes.  These lists are homogeneous
lists, more similar to lists in statically typed functional languages like
ML than Lisp, but support operations very similar to those found in Lisp.
Any particular kind of list class may be generated via the @code{genclass}
shell command. However, the implementation assumes that the base class
supports an equality operator @code{==}.  All equality tests use the
@code{==} operator, and are thus equivalent to the use of @code{equal}, not
@code{eq} in Lisp.@refill

All list nodes are created dynamically, and managed via reference counts.
@code{List} variables are actually pointers to these list nodes.  
Lists may also be traversed via Pixes, as described in the section
describing Pixes. @xref{Pix}

Supported operations are mirrored closely after those in Lisp. Generally,
operations with functional forms are constructive, functional operations,
while member forms (often with the same name) are sometimes
procedural, possibly destructive operations.

As with Lisp, destructive operations are supported. Programmers
are allowed to change head and tail fields in any fashion, creating
circular structures and the like. However, again as with Lisp, some
operations implicitly assume that they are operating on pure lists, and
may enter infinite loops when presented with improper lists. Also, the
reference-counting storage management facility may fail to reclaim
unused circularly-linked nodes. 

Several Lisp-like higher order functions are supported (e.g., @code{map}).
Typedef declarations for the required functional forms are provided
int the @file{.h} file.

For purposes of illustration, assume the specification of class
@code{intList}.  Common Lisp versions of supported operations are shown
in brackets for comparison purposes.

@section Constructors and assignment

@table @code

@item intList a;           [ (setq a nil) ]
Declares a to be a nil intList.

@item intList b(2);        [ (setq b (cons 2 nil)) ]
Declares b to be an intList with a head value of 2, and a nil tail.

@item intList c(3, b);     [ (setq c (cons 3 b)) ]
Declares c to be an intList with a head value of 3, and b as its tail.

@item b = a;               [ (setq b a) ]
Sets b to be the same list as a.

@end table

Assume the declarations of intLists a, b, and c in the following.
@xref{Pix}.

@section List status

@table @code

@item a.null(); OR !a;      [ (null a) ]
returns true if a is null.

@item a.valid();            [ (listp a) ]
returns true if a is non-null. Inside a conditional test, the
@code{void*} coercion may also be used as in @code{if (a) ...}.

@item intList();            [ nil ]
intList() may be used to null terminate a list, as in
@code{intList f(int x) @{if (x == 0) return intList(); ... @} }.

@item a.length();           [ (length a) ]
returns the length of a.

@item a.list_length();      [ (list-length a) ]
returns the length of a, or -1 if a is circular.
@end table

@section heads and tails

@table @code

@item a.get(); OR a.head()  [ (car a) ]
returns a reference to the head field.

@item a[2];                 [ (elt a 2) ]
returns a reference to the second (counting from zero) head field.

@item a.tail();             [ (cdr a) ]
returns the intList that is the tail of a.

@item a.last();             [ (last a) ]
returns the intList that is the last node of a.

@item a.nth(2);             [ (nth a 2) ]
returns the intList that is the nth node of a.

@item a.set_tail(b);        [ (rplacd a b) ]
sets a's tail to b.

@item a.push(2);            [ (push 2 a) ]
equivalent to a = intList(2, a);

@item int x = a.pop()       [ (setq x (car a)) (pop a) ]
returns the head of a, also setting a to its tail.

@end table

@section Constructive operations

@table @code

@item b = copy(a);          [ (setq b (copy-seq a)) ]
sets b to a copy of a.

@item b = reverse(a);       [ (setq b (reverse a)) ]
Sets b to a reversed copy of a.

@item c = concat(a, b);     [ (setq c (concat a b)) ]
Sets c to a concatenated copy of a and b.

@item c = append(a, b);     [ (setq c (append a b)) ]
Sets c to a concatenated copy of a and b. All nodes of a are
copied, with the last node pointing to b.

@item b = map(f, a);        [ (setq b (mapcar f a)) ]
Sets b to a new list created by applying function f to each node
of a.

@item c = combine(f, a, b); 
Sets c to a new list created by applying function f to successive
pairs of a and b. The resulting list has length the shorter of a
and b.

@item b = remove(x, a);     [ (setq b (remove x a)) ]
Sets b to a copy of a, omitting all occurrences of x.

@item b = remove(f, a);     [ (setq b (remove-if f a)) ]
Sets b to a copy of a, omitting values causing function f to
return true.

@item b = select(f, a);     [ (setq b (remove-if-not f a)) ]
Sets b to a copy of a, omitting values causing function f to
return false.

@item c = merge(a, b, f);   [ (setq c (merge a b f)) ]
Sets c to a list containing the ordered elements (using the 
comparison function f) of the sorted lists a and b.

@end table

@section Destructive operations

@table @code

@item a.append(b);          [ (rplacd (last a) b) ]
appends b to the end of a. No new nodes are constructed.

@item a.prepend(b);         [ (setq a (append b a)) ]
prepends b to the beginning of a.

@item a.del(x);             [ (delete x a) ]
deletes all nodes with value x from a.

@item a.del(f);             [ (delete-if f a) ]
deletes all nodes causing function f to return true.

@item a.select(f);          [ (delete-if-not f a) ]
deletes all nodes causing function f to return false.

@item a.reverse();          [ (nreverse a) ]
reverses a in-place.

@item a.sort(f);            [ (sort a f) ]
sorts a in-place using ordering (comparison) function f.

@item a.apply(f);           [ (mapc f a) ]
Applies void function f (int x) to each element of a.

@item a.subst(int old, int repl); [ (nsubst repl old a) ]
substitutes repl for each occurrence of old in a. Note the
different argument order than the Lisp version.

@end table

@section Other operations

@table @code

@item  a.find(int x);       [ (find x a) ]
returns the intList at the first occurrence of x.

@item  a.find(b);           [ (find b a) ]
returns the intList at the first occurrence of sublist b.

@item a.contains(int x);    [ (member x a) ]
returns true if a contains x.

@item a.contains(b);        [ (member b a) ]
returns true if a contains sublist b.

@item a.position(int x);    [ (position x a) ]
returns the zero-based index of x in a, or -1 if x does not occur.

@item int x = a.reduce(f, int base); [ (reduce f a :initial-value base) ]
Accumulates the result of applying int function f(int, int) to
successive elements of a, starting with base.

@end table


@node LinkList, Vector, List, Top
@chapter Linked Lists

SLLists provide pseudo-generic singly linked lists.  DLLists provide
doubly linked lists.  The lists are designed for the simple maintenance
of elements in a linked structure, and do not provide the more extensive
operations (or node-sharing) of class @code{List}. They behave similarly
to the @code{slist} and similar classes described by Stroustrup.@refill

All list nodes are created dynamically. Assignment is performed via
copying.

Class @code{DLList} supports all @code{SLList} operations, plus
additional operations described below.

For purposes of illustration, assume the specification of class
@code{intSLList}. In addition to the operations listed here,
SLLists support traversal via Pixes. @xref{Pix}

@table @code

@item intSLList a;
Declares a to be an empty list.

@item intSLList b = a;
Sets b to an element-by-element copy of a.

@item a.empty()
returns true if a contains no elements

@item a.length();
returns the number of elements in a.

@item a.prepend(x);
places x at the front of the list.

@item a.append(x);
places x at the end of the list.

@item a.join(b)
places all nodes from b to the end of a, simultaneously destroying b.

@item x = a.front()
returns a reference to the item stored at the head of the list, 
or triggers an error if the list is empty.

@item a.rear()
returns a reference to the rear of the list, or triggers an error if the
list is empty.

@item x = a.remove_front()
deletes and returns the item stored at the head of the list.

@item a.del_front()
deletes the first element, without returning it.

@item a.clear()
deletes all items from the list.

@item a.ins_after(Pix i, item);
inserts item after position i. If i is null, insertion is at the front.

@item a.del_after(Pix i);
deletes the element following i. If i is 0, the first item is deleted.

@end table

@section Doubly linked lists

Class @code{DLList} supports the following additional operations,
as well as backward traversal via Pixes.

@table @code

@item x = a.remove_rear();
deletes and returns the item stored at the rear of the list.

@item a.del_rear();
deletes the last element, without returning it.

@item a.ins_before(Pix i, x)
inserts x before the i.

@item a.del(Pix& iint dir = 1)
deletes the item at the current position, then advances forward
if dir is positive, else backward.

@end table

@node Vector, Plex, LinkList, Top
@chapter Vector classes

The files @file{g++-include/Vec.ccP} and @file{g++-include/AVec.ccP}
provide pseudo-generic standard array-based vector operations.  The
corresponding header files are @file{g++-include/Vec.hP} and
@file{g++-include/AVec.hP}.  Class @code{Vec} provides operations
suitable for any base class that includes an equality operator. Subclass
@code{AVec} provides additional arithmetic operations suitable for base
classes that include the full complement of arithmetic operators.

@code{Vecs} are constructed and assigned by copying. Thus, they should
normally be passed by reference in applications programs.

Several mapping functions are provided that allow programmers to
specify operations on vectors as a whole.

For illustrative purposes assume that classes @code{intVec} and
@code{intAVec} have been generated via @code{genclass}.

@section Constructors and assignment

@table @code
@item intVec a;
declares a to be an empty vector. Its size may be changed via resize.

@item intVec a(10);
declares a to be an uninitialized vector of ten elements (numbered 0-9).

@item intVec b(6, 0);
declares b to be a vector of six elements, all initialized to zero. Any
value can be used as the initial fill argument.

@item a = b;
Copies b to a. a is resized to be the same as b.

@item a = b.at(2, 4)
constructs a from the 4 elements of b starting at b[2].
@end table

Assume declarations of @code{intVec a, b, c} and @code{int i, x} in 
the following.

@section Status and access

@table @code
@item a.capacity();
returns the number of elements that can be held in a.

@item a.resize(20);
sets a's length to 20. All elements are unchanged, except that if
the new size is smaller than the original, than trailing elements
are deleted, and if greater, trailing elements are uninitialized.

@item a[i];
returns a reference to the i'th element of a, or produces an error
if i is out of range.

@item a.elem(i)
returns a reference to the i'th element of a. Unlike the @code{[]} operator,
i is not checked to ensure that it is within range.

@item a == b;
returns true if a and b contain the same elements in the same order.

@item a != b;
is the converse of a == b.
@end table

@section Constructive operations

@table @code
@item c = concat(a, b);
sets c to the new vector constructed from all of the elements of
a followed by all of b.

@item c = map(f, a);
sets c to the new vector constructed by applying int function f(int)
to each element of a.

@item c = merge(a, b, f);
sets c to the new vector constructed by merging the elements of
ordered vectors a and b using ordering (comparison) function f.

@item c = combine(f, a, b);
sets c to the new vector constructed by applying int function f(int, int)
to successive pairs of a and b. The result has length the shorter of
a and b.

@item c = reverse(a)
sets c to a, with elements in reverse order.
@end table

@section Destructive operations

@table @code
@item a.reverse();
reverses a in-place.

@item a.sort(f)
sorts a in-place using comparison function f. The sorting method is a 
variation of the quicksort functions supplied with GNU emacs.

@item a.fill(0, 4, 2)
fills the 2 elements starting at a[4] with zero.

@end table

@section Other operations

@table @code

@item a.apply(f)
applies function f to each element in a.

@item x = a.reduce(f, base)
accumulates the results of applying function f to successive elements
of a starting with base.

@item a.index(int targ);
returns the index of the leftmost occurrence of the target, or -1,
if it does not occur.

@item a.error(char* msg)
invokes the error handler. The default version prints the error message,
then aborts.
@end table

@section AVec operations.

AVecs provide additional arithmetic operations.  All vector-by-vector
operators generate an error if the vectors are not the same length. The
following operations are provided, for @code{AVecs a, b} and 
base element (scalar) @code{s}.

@table @code
@item a = b;
Copies b to a. a and b must be the same size.

@item a = s;
fills all elements of a with the value s. a is not resized.

@item a + s; a - s; a * s; a / s
adds, subtracts, multiplies, or divides each element of a with the scalar.

@item a += s; a -= s; a *= s; a /= s;
adds, subtracts, multiplies, or divides the scalar into a.

@item a + b; a - b; product(a, b), quotient(a, b)
adds, subtracts, multiplies, or divides corresponding elements of a and b.

@item a += b; a -= b; a.product(b); a.quotient(b);
adds, subtracts, multiplies, or divides corresponding elements of b into a.

@item s = a * b;
returns the inner (dot) product of a and b.

@item  x = a.sum();
returns the sum of elements of a.

@item x = a.sumsq();
returns the sum of squared elements of a.

@item x = a.min();
returns the minimum element of a.

@item x = a.max();
returns the maximum element of a.

@item i = a.min_index();
returns the index of the minimum element of a.

@item i = a.max_index();
returns the index of the maximum element of a.

Note that it is possible to apply vector versions other arithmetic
operators via the mapping functions. For example, to set vector b
to the  cosines of doubleVec a, use @code{b = map(cos, a);}.
This is often more efficient than performing the operations
in an element-by-element fashion.
@end table

@node Plex, Stack, Vector, Top
@chapter Plex classes

A ``Plex'' is a kind of array with the following properties:

@itemize @bullet
@item
Plexes may have arbitrary upper and lower index bounds. For example
a Plex may be declared to run from indices -10 .. 10.

@item
Plexes may be dynamically expanded at both the lower and upper bounds
of the array in steps of one element.

@item
Only elements that have been specifically initialized or added may
be accessed.

@item
Elements may be accessed via indices. Indices are always checked for
validity at run time.  Plexes may be traversed via simple variations of
standard array indexing loops.

@item
Plex elements may be accessed and traversed via Pixes.

@item
Plex-to-Plex assignment and related operations on entire Plexes
are supported.

@item
Plex classes contain methods to help programmers check the validity
of indexing and pointer operations.

@item
Plexes form ``natural'' base classes for many restricted-access data
structures relying on logically contiguous indices, such as array-based
stacks and queues.

@item
Plexes are implemented as pseudo-generic classes, and must be generated
via the @code{genclass} utility.
@end itemize

Four subclasses of Plexes are supported: A @code{FPlex} is a Plex that
may only grow or shrink within declared bounds; an @code{XPlex} may
dynamically grow or shrink without bounds; an @code{RPlex} is the
same as an @code{XPlex} but better supports indexing with poor
locality of reference; a @code{MPlex} may grow
or shrink, and additionally allows the logical deletion and restoration
of elements. Because these classes are virtual subclasses of the
``abstract'' class @code{Plex}, it is possible to write user code
such as @code{void f(Plex& a) ...} that operates on any kind of
Plex. However, as with nearly any virtual class, specifying the
particular Plex class being used results in more efficient code.

Plexes are implemented as a linked list of @code{IChunks}.  Each chunk
contains a part of the array. Chunk sizes may be specified within Plex
constructors.  Default versions also exist, that use a @code{#define'd}
default.  Plexes grow by filling unused space in existing chunks, if
possible, else, except for FPlexes, by adding another chunk.  Whenever
Plexes grow by a new chunk, the default element constructors (i.e.,
those which take no arguments) for all chunk elements are called at
once. When Plexes shrink, destructors for the elements are not called
until an entire chunk is freed. For this reason, Plexes (like C++
arrays) should only be used for elements with default constructors and
destructors that have no side effects.

Plexes may be indexed and used like arrays, although traversal
syntax is slightly different. Even though Plexes maintain elements
in lists of chunks, they are implemented so that iteration and
other constructs that maintain locality of reference require very
little overhead over that for simple array traversal
Pix-based traversal is also supported. For example, for a plex, p,
of ints, the following traversal methods could be used.

@smallexample
for (int i = p.low(); i < p.fence(); p.next(i)) use(p[i]);
for (int i = p.high(); i > p.ecnef(); p.prev(i)) use(p[i]);
for (Pix t = p.first(); t != 0; p.next(t)) use(p(i));
for (Pix t = p.last(); t != 0; p.prev(t)) use(p(i));
@end smallexample

Except for MPlexes, simply using @code{++i} and @code{--i} works just as
well as @code{p.next(i)} and @code{p.prev(i)} when traversing by index.
Index-based traversal is generally a bit faster than Pix-based
traversal.

@code{XPlexes} and @code{MPlexes} are less than optimal for applications
in which widely scattered elements are indexed, as might occur when
using Plexes as hash tables or ``manually'' allocated linked lists.
In such applications, @code{RPlexes} are often preferable. @code{RPlexes}
use a secondary chunk index table that requires slightly greater,
but entirely uniform overhead per index operation.

Even though they may grow in either direction, Plexes are normally
constructed so that their ``natural'' growth direction is upwards,
in that default chunk construction leaves free space, if present,
at the end of the plex. However, if the chunksize arguments to 
constructors are negative, they leave space at the beginning. 

All versions of Plexes support the following basic capabilities.
(letting @code{Plex} stand for the type name constructed via the
genclass utility (e.g., @code{intPlex}, @code{doublePlex})).  Assume
declarations of @code{Plex p, q}, @code{int i, j}, base element
@code{x}, and Pix @code{pix}.

@table @code

@item Plex p;
Declares p to be an initially zero-sized Plex with low index of zero,
and the default chunk size. For FPlexes, chunk sizes represent maximum
sizes.

@item Plex p(int size);
Declares p to be an initially zero-sized Plex with low index of zero,
and the indicated chunk size. If size is negative, then the Plex
is created with free space at the beginning of the Plex,
allowing more efficient add_low() operations. Otherwise, it
leaves space at the end.

@item Plex p(int low, int size);
Declares p to be an initially zero-sized Plex with low index of low,
and the indicated chunk size.

@item Plex p(int low, int high, Base initval, int size = 0);
Declares p to be a Plex with indices from low to high, initially
filled with initval, and the indicated chunk size if specified,
else the default or (high - low + 1), whichever is greater. 

@item Plex q(p);
Declares q to be a copy of p.

@item p = q;
Copies Plex q into p, deleting its previous contents.

@item p.length()
Returns the number of elements in the Plex.

@item p.empty()
Returns true if Plex p contains no elements.

@item p.full()
Returns true if Plex p cannot be expanded. This always returns
false for XPlexes and MPlexes.

@item p[i]
Returns a reference to the i'th element of p. An exception (error) occurs
if i is not a valid index. 

@item p.valid(i)
Returns true if i is a valid index into Plex p.

@item p.low(); p.high();
Return the minimum (maximum) valid index of the Plex, or the high (low)
fence if the plex is empty.

@item p.ecnef(); p.fence();
Return the index one position past the minimum (maximum) valid index.

@item p.next(i); i = p.prev(i);
Set i to the next (previous) index. This index may not be within bounds.

@item p(pix)
returns a reference to the item at Pix pix.

@item pix = p.first(); pix = p.last();
Return the minimum (maximum) valid Pix of the Plex, or 0
if the plex is empty.

@item p.next(pix); p.prev(pix);
set pix to the next (previous) Pix, or 0 if there is none.

@item p.owns(pix)
Returns true if the Plex contains the element associated with pix.

@item p.Pix_to_index(pix)
If pix is a valid Pix to an element of the Plex, 
returns its corresponding index, else raises an exception. 

@item ptr = p.index_to_Pix(i)
if i is a valid index, returns a the corresponding Pix.

@item p.low_element(); p.high_element();
Return a reference to the element at the minimum (maximum) valid index.
An exception occurs if the Plex is empty.

@item  p.can_add_low();  p.can_add_high();
Returns true if the plex can be extended one element downward (upward).
These always return true for XPlex and MPlex.

@item j = p.add_low(x); j = p.add_high(x);
Extend the Plex by one element downward (upward). The new minimum
(maximum) index is returned.

@item j = p.del_low(); j = p.del_high()
Shrink the Plex by one element on the low (high) end. The new
minimum (maximum) element is returned. An exception occurs if the
Plex is empty.

@item p.append(q);
Append all of Plex q to the high side of p.

@item p.prepend(q);
Prepend all of q to the low side of p.

@item p.clear()
Delete all elements, resetting p to a zero-sized Plex.

@item p.reset_low(i);
Resets p to be indexed starting at low() = i. For example.
if p were initially declared via @code{Plex p(0, 10, 0)}, 
and then re-indexed via @code{p.reset_low(5)}, 
it could then be indexed from indices 5 .. 14.

@item p.fill(x)
sets all p[i] to x.

@item p.fill(x, lo, hi)
sets all of p[i] from lo to hi, inclusive, to x.

@item p.reverse()
reverses p in-place.

@item p.chunk_size()
returns the chunk size used for the plex.

@item p.error(const char * msg)
calls the resettable error handler.

@end table

MPlexes are plexes with bitmaps that allow items to be logically
deleted and restored. They behave like other plexes, but
also support the following additional and modified capabilities:

@table @code

@item p.del_index(i); p.del_Pix(pix)
logically deletes p[i] (p(pix)). After deletion, attempts to access p[i]
generate a error. Indexing via low(), high(), prev(),
and next() skip the element. Deleting an element never changes the
logical bounds of the plex. 

@item p.undel_index(i); p.undel_Pix(pix)
logically undeletes p[i] (p(pix)). 

@item p.del_low(); p.del_high()
Delete the lowest (highest) undeleted element, resetting the
logical bounds of the plex to the next lowest (highest) undeleted
index. Thus, MPlex del_low() and del_high() may shrink the bounds
of the plex by more than one index.

@item p.adjust_bounds()
Resets the low and high bounds of the Plex to the indexes of
the lowest and highest actual undeleted elements.

@item int i = p.add(x)
Adds x in an unused index, if possible, else performs add_high.

@item p.count()
returns the number of valid (undeleted) elements.

@item p.available()
returns the number of available (deleted) indices.

@item int i = p.unused_index()
returns the index of some deleted element, if one exists, 
else triggers an error. An unused element may be reused via undel.

@item pix = p.unused_Pix()
returns the pix of some deleted element, if one exists, else 0.
An unused element may be reused via undel.

@end table

@node Stack, Queue, Plex, Top
@chapter Stacks

Stacks are declared as an ``abstract'' class. They are currently
implemented in any of three ways.

@table @code

@item VStack
implement fixed sized stacks via arrays.

@item XPStack 
implement dynamically-sized stacks via XPlexes.

@item SLStack
implement dynamically-size stacks via linked lists.

@end table

All possess the same capabilities. They differ only in constructors.
VStack constructors require a fixed maximum capacity argument. 
XPStack constructors optionally take a chunk size argument.
SLStack constructors take no argument.

Assume the declaration of a base element @code{x}.

@table @code

@item Stack s;  or Stack s(int capacity)
declares a Stack.

@item s.empty()
returns true if stack s is empty.

@item s.full()
returns true if stack s is full. XPStacks and SLStacks never become full.

@item s.length()
returns the current number of elements in the stack.

@item s.push(x)
pushes x on stack s.

@item x = s.pop()
pops and returns the top of stack

@item s.top()
returns a reference to the top of stack.

@item s.del_top()
pops, but does not return the top of stack. When large items are held
on the stack it is often a good idea to use @code{top()} to inspect and use
the top of stack, followed by a @code{del_top()}

@item s.clear()
removes all elements from the stack.

@end table

@node Queue, Deque, Stack, Top
@chapter Queues

Queues are declared as an ``abstract'' class. They are currently
implemented in any of three ways.

@table @code
@item VQueue 
implement fixed sized Queues via arrays.

@item XPQueue 
implement dynamically-sized Queues via XPlexes.

@item SLQueue 
implement dynamically-size Queues via linked lists.
@end table

All possess the same capabilities; they differ only in constructors.
@code{VQueue} constructors require a fixed maximum capacity argument. 
@code{XPQueue} constructors optionally take a chunk size argument.
@code{SLQueue} constructors take no argument.

Assume the declaration of a base element @code{x}.

@table @code
@item Queue q; or Queue q(int capacity);
declares a queue.

@item q.empty()
returns true if queue q is empty.

@item q.full()
returns true if queue q is full. XPQueues and SLQueues are never full.

@item q.length()
returns the current number of elements in the queue.

@item q.enq(x)
enqueues x on queue q.

@item x = q.deq()
dequeues and returns the front of queue

@item q.front()
returns a reference to the front of queue.

@item q.del_front()
dequeues, but does not return the front of queue

@item q.clear()
removes all elements from the queue.
@end table

@node Deque, PQ, Queue, Top
@chapter Double ended Queues

Deques are declared as an ``abstract'' class. They are currently
implemented in two ways.

@table @code

@item XPDeque
implement dynamically-sized Deques via XPlexes.

@item DLDeque
implement dynamically-size Deques via linked lists.

@end table

All possess the same capabilities. They differ only in constructors.
XPDeque constructors optionally take a chunk size argument.
DLDeque constructors take no argument.

Double-ended queues support both stack-like and queue-like capabilities:

Assume the declaration of a base element @code{x}.

@table @code

@item Deque d; or Deque d(int initial_capacity)
declares a deque.

@item d.empty()
returns true if deque d is empty.

@item d.full()
returns true if deque d is full. 
Always returns false in current implementations.

@item d.length()
returns the current number of elements in the deque.

@item d.enq(x)
inserts x at the rear of deque d.

@item d.push(x)
inserts x at the front of deque d.

@item x = d.deq()
dequeues and returns the front of deque

@item d.front()
returns a reference to the front of deque.

@item d.rear()
returns a reference to the rear of the deque.

@item d.del_front()
deletes, but does not return the front of deque

@item d.del_rear()
deletes, but does not return the rear of the deque.

@item d.clear()
removes all elements from the deque.

@end table

@node  PQ, Set, Deque, Top
@chapter Priority Queue class prototypes.

Priority queues maintain collections of objects arranged for fast
access to the least element.

Several prototype implementations of priority queues are supported.

@table @code

@item XPPQs 
implement 2-ary heaps via XPlexes.

@item SplayPQs 
implement  PQs via Sleator and Tarjan's (JACM 1985)
splay trees. The algorithms use a version of ``simple top-down
splaying'' (described on page 669 of the article).  The simple-splay
mechanism for priority queue functions is loosely based on the one used
by D. Jones in the C splay tree functions available from volume 14 of
the uunet.uu.net archives.

@item PHPQs 
implement pairing heaps (as described by Fredman and
Sedgewick in @cite{Algorithmica}, Vol 1, p111-129).  Storage for heap elements
is managed via an internal freelist technique. The constructor allows an
initial capacity estimate for freelist space.  The storage is automatically
expanded if necessary to hold new items. The deletion technique is a fast
``lazy deletion'' strategy that marks items as deleted, without reclaiming
space until the items come to the top of the heap. 

@end table

All PQ classes support the following operations, for some PQ class
@code{Heap}, instance @code{h}, @code{Pix ind}, and base class
variable @code{x}.

@table @code

@item h.empty()
returns true if there are no elements in the PQ.

@item h.length()
returns the number of elements in h.

@item ind = h.enq(x)
Places x in the PQ, and returns its index.

@item x = h.deq()
Dequeues the minimum element of the PQ into x, or generates an error
if the PQ is empty.

@item h.front()
returns a reference to the minimum element.

@item h.del_front()
deletes the minimum element.

@item h.clear();
deletes all elements from h;

@item h.contains(x)
returns true if x is in h.

@item h(ind)
returns a reference to the item indexed by ind.

@item ind = h.first()
returns the Pix of first item in the PQ or 0 if empty. 
This need not be the Pix of the least element.

@item h.next(ind)
advances ind to the Pix of next element, or 0 if there are no more.

@item ind = h.seek(x)
Sets ind to the Pix of x, or 0 if x is not in h.

@item h.del(ind)
deletes the item with Pix ind.

@end table

@node Set, Bag, PQ, Top
@chapter Set class prototypes

Set classes maintain unbounded collections of items containing 
no duplicate elements.

These are currently implemented in several ways, differing in
representation strategy, algorithmic efficiency, and appropriateness for
various tasks. (Listed next to each are average (followed by worst-case,
if different) time complexities for [a] adding, [f] finding (via seek,
contains), [d] deleting, elements, and [c] comparing (via ==, <=) and
[m] merging (via |=, -=, &=) sets).

@table @code
@item XPSets 
implement unordered sets via XPlexes. 
([a O(n)], [f O(n)], [d O(n)], [c O(n^2)] [m O(n^2)]).

@item OXPSets 
implement ordered sets via XPlexes.
([a O(n)], [f O(log n)], [d O(n)], [c O(n)] [m O(n)]).

@item SLSets 
implement unordered sets via linked lists
([a O(n)], [f O(n)], [d O(n)], [c O(n^2)] [m O(n^2)]).

@item OSLSets 
implement ordered sets via linked lists
([a O(n)], [f O(n)], [d O(n)], [c O(n)] [m O(n)]).

@item AVLSets 
implement ordered sets via threaded AVL trees
([a O(log n)], [f O(log n)], [d O(log n)], [c O(n)] [m O(n)]).

@item BSTSets 
implement ordered sets via binary search trees. The trees may
be manually rebalanced via the O(n) @code{balance()} member function.
([a O(log n)/O(n)], [f O(log n)/O(n)], [d O(log n)/O(n)], [c O(n)] [m O(n)]).

@item SplaySets 
implement ordered sets via Sleator and Tarjan's (JACM 1985)
splay trees. The algorithms use a version of ``simple top-down
splaying'' (described on page 669 of the article).  
(Amortized: [a O(log n)], [f O(log n)], [d O(log n)], [c O(n)] [m O(n log n)]).

@item VHSets 
implement unordered sets via hash tables.
The tables are automatically resized when their capacity is exhausted.
([a O(1)/O(n)], [f O(1)/O(n)], [d O(1)/O(n)], [c O(n)/O(n^2)] [m O(n)/O(n^2)]).

@item VOHSets 
implement unordered sets via ordered hash tables
The tables are automatically resized when their capacity is exhausted.
([a O(1)/O(n)], [f O(1)/O(n)], [d O(1)/O(n)], [c O(n)/O(n^2)] [m O(n)/O(n^2)]).

@item CHSets 
implement unordered sets via chained hash tables.
([a O(1)/O(n)], [f O(1)/O(n)], [d O(1)/O(n)], [c O(n)/O(n^2)] [m O(n)/O(n^2)]).
@end table

The different implementations differ in whether their constructors
require an argument specifying their initial capacity. Initial
capacities are required for plex and hash table based Sets.  If none is
given @code{DEFAULT_INITIAL_CAPACITY} (from @file{<T>defs.h}) is
used.@refill

Sets support the following operations, for some class @code{Set},
instances @code{a} and @code{b}, @code{Pix ind}, and base 
element @code{x}. Since all implementations are virtual derived classes
of the @code{<T>Set} class, it is possible to mix and match operations
across different implementations, although, as usual, operations
are generally faster when the particular classes are specified
in functions operating on Sets. 

Pix-based operations are more fully described in the section
on Pixes. @xref{Pix}

@table @code

@item Set a; or Set a(int initial_size);
Declares a to be an empty Set. The second version is allowed in
set classes that require initial capacity or sizing specifications.

@item a.empty()
returns true if a is empty.

@item a.length()
returns the number of elements in a.

@item Pix ind = a.add(x)
inserts x into a, returning its index.

@item a.del(x)
deletes x from a.

@item a.clear()
deletes all elements from a;

@item a.contains(x)
returns true if x is in a.

@item a(ind)
returns a reference to the item indexed by ind.

@item ind = a.first()
returns the Pix of first item in the set or 0 if the Set is empty. 
For ordered Sets, this is the Pix of the least element.

@item a.next(ind)
advances ind to the Pix of next element, or 0 if there are no more.

@item ind = a.seek(x)
Sets ind to the Pix of x, or 0 if x is not in a.

@item a == b
returns true if a and b contain all the same elements.

@item a != b
returns true if a and b do not contain all the same elements.

@item a <= b
returns true if a is a subset of b.

@item a |= b
Adds all elements of b to a. 

@item a -= b
Deletes all elements of b from a.

@item a &= b
Deletes all elements of a not occurring in b.

@end table


@node Bag, Map, Set, Top
@chapter Bag class prototypes

Bag classes maintain unbounded collections of items potentially
containing  duplicate elements.

These are currently implemented in several ways, differing in
representation strategy, algorithmic efficiency, and appropriateness for
various tasks. (Listed next to each are average (followed by worst-case,
if different) time complexities for [a] adding, [f] finding (via seek,
contains), [d] deleting elements).


@table @code

@item XPBags 
implement unordered Bags via XPlexes.
([a O(1)], [f O(n)], [d O(n)]).

@item OXPBags 
implement ordered Bags via XPlexes.
([a O(n)], [f O(log n)], [d O(n)]).

@item SLBags 
implement unordered Bags via linked lists
([a O(1)], [f O(n)], [d O(n)]).

@item OSLBags 
implement ordered Bags via linked lists
([a O(n)], [f O(n)], [d O(n)]).

@item SplayBags 
implement ordered Bags via Sleator and Tarjan's (JACM 1985)
splay trees. The algorithms use a version of ``simple top-down
splaying'' (described on page 669 of the article).
(Amortized: [a O(log n)], [f O(log n)], [d O(log n)]).

@item VHBags 
implement unordered Bags via hash tables.
The tables are automatically resized when their capacity is exhausted.
([a O(1)/O(n)], [f O(1)/O(n)], [d O(1)/O(n)]).

@item CHBags 
implement unordered Bags via chained hash tables.
([a O(1)/O(n)], [f O(1)/O(n)], [d O(1)/O(n)]).

@end table

The implementations differ in whether their constructors
require an argument to specify their initial capacity. Initial
capacities are required for plex and hash table based Bags.  If none is
given @code{DEFAULT_INITIAL_CAPACITY} (from @file{<T>defs.h}) is used.@refill

Bags support the following operations, for some class @code{Bag},
instances @code{a} and @code{b}, @code{Pix ind}, and base 
element @code{x}. Since all implementations are virtual derived classes
of the @code{<T>Bag} class, it is possible to mix and match operations
across different implementations, although, as usual, operations
are generally faster when the particular classes are specified
in functions operating on Bags. 

Pix-based operations are more fully described in the section
on Pixes. @xref{Pix}

@table @code

@item Bag a; or Bag a(int initial_size)
Declares a to be an empty Bag. The second version is allowed in
Bag classes that require initial capacity or sizing specifications.

@item a.empty()
returns true if a is empty.

@item a.length()
returns the number of elements in a.

@item ind = a.add(x)
inserts x into a, returning its index.

@item a.del(x)
deletes one occurrence of x from a.

@item a.remove(x)
deletes all occurrences of x from a.

@item a.clear()
deletes all elements from a;

@item a.contains(x)
returns true if x is in a.

@item a.nof(x)
returns the number of occurrences of x in a.

@item a(ind)
returns a reference to the item indexed by ind.

@item int = a.first()
returns the Pix of first item in the Bag or 0 if the Bag is empty. 
For ordered Bags, this is the Pix of the least element.

@item a.next(ind)
advances ind to the Pix of next element, or 0 if there are no more.

@item ind = a.seek(x. Pix from = 0)
Sets ind to the Pix of the next occurrence x, or 0 if there are none.
If from is 0, the first occurrence is returned, else the following from.

@end table

@node  Map, GetOpt, Bag, Top
@chapter Map Class Prototypes

Maps support associative array operations (insertion, deletion, and
membership of records based on an associated key). They require
the specification of two types, the key type and the contents type.

These are currently implemented in several ways, differing in
representation strategy, algorithmic efficiency, and appropriateness for
various tasks. (Listed next to each are average (followed by worst-case,
if different) time complexities for [a] accessing (via op [],
contains), [d] deleting elements).


@table @code

@item AVLMaps 
implement ordered Maps via threaded AVL trees
([a O(log n)], [d O(log n)]).

@item RAVLMaps 
Similar, but also maintain ranking information, used via 
@code{ranktoPix(int r)}, that returns the @code{Pix} of the
item at rank r, and @code{rank(key)} that returns the
rank of the corresponding item.
([a O(log n)], [d O(log n)]).

@item SplayMaps 
implement ordered Maps via Sleator and Tarjan's (JACM 1985)
splay trees. The algorithms use a version of ``simple top-down
splaying'' (described on page 669 of the article).  
(Amortized: [a O(log n)], [d O(log n)]).

@item VHMaps 
implement unordered Maps via hash tables.
The tables are automatically resized when their capacity is exhausted.
([a O(1)/O(n)], [d O(1)/O(n)]).

@item CHMaps 
implement unordered Maps via chained hash tables.
([a O(1)/O(n)], [d O(1)/O(n)]).

@end table

The different implementations differ in whether their constructors
require an argument specifying their initial capacity. Initial
capacities are required for hash table based Maps.  If none is
given @code{DEFAULT_INITIAL_CAPACITY} (from @file{<T>defs.h}) is
used.@refill

All Map classes share the following operations (for some Map class,
@code{Map} instance @code{d}, @code{Pix ind} and key variable @code{k},
and contents variable @code{x}).

Pix-based operations are more fully described in the section
on Pixes. @xref{Pix}

@table @code

@item Map d(x);  Map d(x, int initial_capacity)
Declare d to be an empty Map. The required argument, x, specifies
the default contents, i.e., the contents of an otherwise
uninitialized location. The second version, specifying
initial capacity is allowed for Maps with an initial capacity
argument.

@item d.empty()
returns true if d contains no items.

@item d.length()
returns the number of items in d.

@item d[k]
returns a reference to the contents of item with key k. If no
such item exists, it is installed with the default contents.
Thus d[k] = x installs x, and x = d[k] retrieves it. 

@item  d.contains(k)
returns true if an item with key field k exists in d.

@item d.del(k)
deletes the item with key k.

@item d.clear()
deletes all items from the table.

@item x = d.dflt()
returns the default contents.

@item k = d.key(ind)
returns a reference to the key at Pix ind.

@item x = d.contents(ind)
returns a reference to the contents at Pix ind.

@item ind = d.first()
returns the Pix of the first element in d, or 0 if d is empty.

@item d.next(ind)
advances ind to the next element, or 0 if there are no more.

@item ind = d.seek(k)
returns the Pix of element with key k, or 0 if k is not in d.

@end table

@node GetOpt, Projects, Map, Top
@chapter C++ version of the GNU getopt function

The GetOpt class provides an efficient and structured mechanism for
processing command-line options from an application program.  The sample
program fragment below illustrates a typical use of the GetOpt class
for some hypothetical application program:

@smallexample
#include <stdio.h>
#include <GetOpt.h>
//...
int debug_flag, compile_flag, size_in_bytes;

int
main (int argc, char **argv)
@{
  // Invokes ctor `GetOpt (int argc, char **argv, 
  //                       char *optstring);'
  GetOpt getopt (argc, argv, "dcs:");
  int option_char;
  
  // Invokes member function `int operator ()(void);'
  while ((option_char = getopt ()) != EOF)
    switch (option_char)
      @{  
         case 'd': debug_flag = 1; break;
         case 'c': compile_flag = 1; break;
         case 's': size_in_bytes = atoi (getopt.optarg); break;
         case '?': fprintf (stderr, 
                            "usage: %s [dcs<size>]\n", argv[0]);
      @}
@}
@end smallexample

Unlike the C library version, the libg++ GetOpt class uses its
constructor to initialize class data members containing the argument
count, argument vector, and the option string.  This simplifies the
interface for each subsequent call to member function @code{int operator
()(void)}.

The C version, on the other hand, uses hidden static variables to retain
the option string and argument list values between calls to
@code{getopt}.  This complicates the @code{getopt} interface since the
argument count, argument vector, and option string must be passed as
parameters for each invocation.  For the C version, the loop in the
previous example becomes:

@smallexample
  while ((option_char = getopt (argc, argv, "dcs:")) != EOF)
    // ...
@end smallexample

which requires extra overhead to pass the parameters for every call.

Along with the GetOpt constructor and @code{int operator ()(void)},
the other relevant elements of class GetOpt are:

@table @code
@item char *optarg
Used for communication from @code{operator ()(void)} to the caller.
When @code{operator ()(void)} finds an option that takes an argument, the
argument value is stored here.
@item int optind
Index in @code{argv} of the next element to be scanned.
This is used for communication to and from the caller
and for communication between successive calls to @code{operator ()(void)}.
          
When @code{operator ()(void)} returns EOF, this is the index of the
first of the non-option elements that the caller should itself scan.
              
Otherwise, @code{optind} communicates from one call to the next how much
of @code{argv} has been scanned so far.
@end table

The libg++ version of GetOpt acts like standard UNIX @code{getopt} for
the calling routine, but it behaves differently for the user, since it
allows the user to intersperse the options with the other arguments.
      
As GetOpt works, it permutes the elements of @code{argv} so that, when
it is done, all the options precede everything else.  Thus all
application programs are extended to handle flexible argument order.

Setting the environment variable _POSIX_OPTION_ORDER disables
permutation.  Then the behavior is completely standard.

@ignore
((Left out because it is not part of libg++ proper, and does not
use the library copyright.))

@node Gperf, Projects, GetOpt, Top
@chapter A Perfect Hash Function Generator

GNU GPERF is a utility program that automatically generates perfect hash
functions from a list of keywords.  The GNU C, GNU C++, GNU Pascal, GNU
Modula 3 compilers and the GNU indent code formatting program all
utilize reserved word recognizer routines generated by GPERF.  Complete
documentation and source code is available in the ./gperf subdirectory
in the libg++ distribution.  A paper describing GPERF in detail is
available in the proceedings of the USENIX Second C++ Conference.
@end ignore

@node Projects, , GetOpt, Top
@chapter Projects and other things left to do

@section Coming Attractions

Some things that will probably be available in libg++ in the near future:

@itemize @bullet

@item
Revamped C-compatibility header files that will be compatible with
the forthcoming (ANSI-based) GNU libc.a

@item
A revision of the File-based classes that will use the GNU stdio library,
and also be 100% compatible (even at the streambuf level) with the AT&T
2.0 stream classes.

@item
Additional container class prototypes.

@item
generic Matrix class prototypes.

@item
A task package probably based on Dirk Grunwald's threads package.

@end itemize

@section Wish List

Some things that people have mentioned that they would like to
see in libg++, but for which there have not been any offers:

@itemize @bullet

@item
A method to automatically convert or incorporate libg++ classes
so they can be used directly in Gorlen's OOPS environment.

@item
A class browser.

@item
A better general exception-handling strategy.

@item
Better documentation.

@end itemize

@section How to contribute

Programmers who have written C++ classes that they believe to
be of general interest are encourage to write to dl at rocky.oswego.edu.
Contributing code is not difficult. Here are some general guidelines:

@itemize @bullet

@item
FSF must maintain the right to accept or reject potential contributions.
Generally, the only reasons for rejecting contributions are cases where
they duplicate existing or nearly-released code, contain unremovable
specific machine dependencies, or are somehow incompatible with the
rest of the library. 

@item
Acceptance of contributions means that the code is accepted for adaptation
into libg++.  FSF must reserve the right to make various editorial changes
in code. Very often, this merely entails formatting, maintenance of various
conventions, etc. Contributors are always given authorship credit and shown
the final version for approval.

@item
Contributors must assign their copyright to FSF via a form sent out
upon acceptance. Assigning copyright to FSF ensures that the code
may be freely distributed.

@item
Assistance in providing documentation, test files, and debugging
support is strongly encouraged.

@end itemize

Extensions, comments, and suggested modifications of existing libg++
features are also very welcome.
@contents
@bye
