README

/*! \file libaff/README
 * \brief C++ containers for numbers (libaff)
 *
 * ----------------------------------------------------------------------------
 *
 * $Id: README,v 1.19 2003-01-02 11:53:30 forbrig Exp $
 * 
 * Copyright (c) 2002 by Thomas Forbriger (IMG Frankfurt) 
 * 
 * C++ containers for numbers (libaff)
 *
 * This file contains:
 *  - documentation of namespace aff
 *  - mainpage text
 *  - documentation for pages:
 *    - \ref page_design
 *    - \ref page_using
 *    - \ref page_notes
 *    - \ref page_naming
 * 
 * REVISIONS and CHANGES 
 *  - 06/12/2002   V1.0   Thomas Forbriger (copied from libcontxx)
 *  - 20/12/2002   V1.1   (thof)
 *                        - complete revision of this file
 *                        - there are major gaps in
 *                          -# \ref sec_design_multidimensional
 *                          -# \ref page_using
 *  - 28/12/2002   V1.2   (thof)
 *                        - new term for containers of const elements
 *                        - added documentation regarding the concept of 
 *                          const correctness
 *                        - added documentation regarding member typedefs
 *  - 29/12/2002   V1.3   (thof)
 *                        - added section about replicated shared heap base
 *                          class (\ref sec_design_replicated)
 *                        - added section about sparse interface
 *                          (\ref sec_design_interface_sparse)
 *                        - added section about accessing internals
 *                          (\ref sec_design_interface_internals)
 *                        - reflect changes to Subarray and Slice
 *                        - tell about class hierarchies and member data vs.
 *                          inheritance
 * 
 * ============================================================================
 */

/*! \brief Root namespace of library
  
  This namespace contains all modules of the library
  (see \ref sec_main_modules). 
  Here you should find all components, the user needs to work with this
  library.
  When working with the binary version of the library, you have to use
  aff::prebuilt in place of aff (see \ref sec_design_binary).
 */
namespace aff {
} // namespace aff

/*======================================================================*/

/*! \mainpage

\author Thomas Forbriger
\author Wolfgang Friederich
\since December 2002
\date December 2002
\version V1.0
$Id: README,v 1.19 2003-01-02 11:53:30 forbrig Exp $

  Contents of this page:
  - \ref sec_main_aims
  - \ref sec_main_modules
    - \ref sec_main_modules_basic
    - \ref sec_main_modules_extended
  - \ref sec_main_peculiar

  Additional information:
  - \ref page_design
  - \ref page_using
  - \ref page_notes
  - \ref page_naming
  - \ref page_representation
  - \ref page_fortran
  - \ref page_changelog
  - \ref page_project_status

\section sec_main_aims Aims of the library
  
  The AFF (Array of Friederich and Forbriger) is a lightweight class library.
  It offers a simple and easy to use container for numbers as is necessary in
  numerical code. The offered array always has a rectangular strided layout,
  reference semantics (through counted references) and a Fortran layout in
  memory. The interface is intentionally kept sparse to keep compilation times
  small. The array itself is meant to be used to pass numbers from one program
  module to the other. If you want to exploit the power of expression
  templates, pass the array contents to something like Blitz++.

  \sa \ref sec_notes_need

/*----------------------------------------------------------------------*/

\section sec_main_modules Modules of the library

  The main module is the array class aff::Array. It provides basic
  functionality through its interface. See the explanation there.
  It is presented in aff/array.h and aff/binarray.h (see also 
  \ref sec_design_binary).
  The object code is placed in libaff.a.

\subsection sec_main_modules_basic Basic array modules

  By including aff/array.h you will get access to the following modules:

  -# aff::Array is the main array interface (see example tests/arraytest.cc).
  -# aff::Strided is the shape of a strided Fortran array and defines the
                memory layout of aff::Array objects (see example
                tests/shapetest.cc).
  -# aff::SharedHeap is the representation used by aff::Array. It holds the
                data in memory and provides an interface to it. This interface
                may be passed separately from the array object (see also
                "\ref page_representation" and example tests/reprtest.cc).
  -# aff::SimpleRigidArray is a linear array with size fixed at compile-time.
                There are several inline functions defined for operations with
                this array class (see example tests/simplearraytest.cc).
  -# aff::Exception is the exception base class used in the library.
  -# aff::AllocException is the exception that indicated a failed memory
                allocation(see also "\ref group_error").

  It additionally offers the following type definitions:

  -# aff::Tsubscript is the type of subscripts to arrays (positive and
                     negative).
  -# aff::Tsize      is the type of size values (non-negative).
  -# aff::Tdim       is the type of the dimension index (small, non-negative).

\subsection sec_main_modules_extended Extensions
  
  The library provides some additional modules. You need only include the
  header file of those modules that you really want to use in addition to the
  basic aff::Array functionality.
  These additional modules are:

  -# aff::Shaper presented in aff/shaper.h and used to pass Fortran layouts
                 to array constructors (see example tests/shapetest.cc).
  -# aff::Series presented in aff/series.h which is used to interface linear
                 sequences of data (like time series or Fourier spectra).
  -# aff::Iterator presented in aff/iterator.h which is an iterator interface
                 to containers like aff::Array or aff::Series (see example
                 tests/helpertest.cc).
  -# aff::Range presented in aff/lib/range.h which is usefull where ever you
                 need to deal with numerical ranges (calculate with them, find 
                 the smallest in a set, etc.).
  -# aff::subarray presented in aff/subarray.h to conveniently create
                 subarrays from aff::Array objects (see example
                 tests/helpertest.cc).
  -# aff::slice presented in aff/slice.h to conveniently create
                 slices from aff::Array objects (see example
                 tests/helpertest.cc).
  -# aff::FortranArray and its associate aff::util::FortranShape are presented
                 in aff/fortranshape.h. They calculate a Fortran 77 array
                 layout (leading dimensions) from a given AFF array (see
                 example tests/f77test.cc).
  -# aff::dump and its associates, presented in aff/dump.h. They are used to 
                 dump shape or contents of containers and are thus useful when
                 debugging your code. See also "\ref group_helpers".


  In the \ref sec_design_binary "binary version" some of the modules
  (aff::Array and aff::SharedHeap) are presented in namespace aff::prebuilt.

  \sa \ref sec_design_namespaces
  \sa \ref sec_naming_files

/*----------------------------------------------------------------------*/

\section sec_main_peculiar Peculiarities

\par Containers use counted references
All containers (e.g. aff::Array, aff::Series) use counted references to access
global memory. Assigning one container object to another just assigns the
reference. Both will use the same data in memory afterwards. 
See also "\ref page_representation".

\par Const-correctness for array elements
In this library we follow provide functionality to write const-correct code
with regard to the array container and with regard to its element values.
See also "\ref sec_design_const".

\par Multidimensional arrays
Every aff::Array of this class has aff::Strided::Mmax_dimen dimensions.
Construction and access for lower dimensionality is provided. In the case of
using less dimensions, the size of the unused dimensions is 1 by default and
its index is inherently set to the first index.
See also "\ref sec_design_multidimensional".

*/

/*======================================================================*/

/*! \page page_design Design decisions

  Contents of this page:
  - \ref sec_design_interface
    - \ref sec_design_interface_sparse
    - \ref sec_design_interface_typedef
    - \ref sec_design_interface_internals
  - \ref sec_design_hierarchy
  - \ref sec_design_replicated
    - \ref sec_design_replicated_fact
    - \ref sec_design_replicated_problem
    - \ref sec_design_replicated_solution
  - \ref sec_design_copy
  - \ref sec_design_namespaces
  - \ref sec_design_binary
  - \ref sec_design_multidimensional
  - \ref sec_design_const
    - \ref sec_design_const_problem
    - \ref sec_design_const_approach
    - \ref sec_design_const_alternatives
    - \ref sec_design_const_general

\section sec_design_interface Common interface concepts

\subsection sec_design_interface_sparse Sparse interfaces

  The class library is intended to be a  light-weight library. This means it
  should offer basic functionality in terms of multidimensional containers
  with counted references (and not more in first place). We do not like to
  include a tremendous amount of code for specialized concepts (like subranges
  or expression templates in Blitz++) each time we just need a small array.
  Thus the header files providing array declarations (aff/array.h and the
  files included therein) should be as sparse as possible. All extra
  functionality like iterators (aff::Iterator presented in aff/iterator.h) or
  slices (aff::Slice presented in aff/slice.h) should be external to the
  aff::Array class. This allows us to load their definitions only where
  needed. However, this approach requires that the internals of aff::Array are
  exposed to the outside through appropriate functions (see "\ref
  sec_design_interface_internals").

\subsection sec_design_interface_typedef Member typedefs

  Class templates like aff::Iterator may be used with any container class,
  that provides an appropriate interface. This interface convention concerns
  the access to the type of related objects. I will explain by example:

  We use an iterator \c i which was declared
  \code aff::Iterator<Cont> i \endcode
  for a container of type \c Cont, it expects to find a corresponding
  container class that promises constness of the elements through 
  \code Cont::Tcontainer_of_const \endcode
  or short
  \code Cont::Tcoc \endcode

  For aff::ConstArray the type aff::ConstArray::Tcoc is just the class itself.
  However aff::Array::Tcoc gives an aff::ConstArray.

  \sa aff::SharedHeap::Tcontainer_of_const
  \sa aff::ConstSharedHeap::Tcontainer_of_const
  \sa aff::Array::Tcontainer_of_const
  \sa aff::ConstArray::Tcontainer_of_const
  \sa aff::Series::Tcontainer_of_const
  \sa aff::ConstSeries::Tcontainer_of_const

  In the same way we may access the appropriate element type through
  \code Cont::Tvalue \endcode
  which is \c T for aff::Array<T> and \c const \T for aff::ConstArray<T>.
  However a 
  \code Cont::Tconst_value \endcode
  will always provide a type with const qualifier.

  \sa aff::Array::Tvalue
  \sa aff::Array::Tconst_value
  \sa aff::ConstArray::Tvalue
  \sa aff::ConstArray::Tconst_value
  \sa aff::Series::Tvalue
  \sa aff::Series::Tconst_value
  \sa aff::ConstSeries::Tvalue
  \sa aff::ConstSeries::Tconst_value

  In the same way we may access the type of the appropriate representation
  (although the base class of any container is always an aff::SharedHeap) by
  \code Cont::Trepresentation \endcode

  \sa aff::Array::Trepresentation
  \sa aff::ConstArray::Trepresentation
  \sa aff::Series::Trepresentation
  \sa aff::ConstSeries::Trepresentation

  \b Notice: Using these typedefs (and also the typedefs for the shape class,
  etc.) improves the maintainability of your code. Think of using the $HOME
  variable in shell scripts. Once the name of your home directory changes, you
  need not modify all your shell scripts. Now consider one day your shape
  class might be renamed...

\subsection sec_design_interface_internals Accessing internals

  Providing extended functionality outside of aff::Array (see 
  "\ref sec_design_interface_sparse") requires, that aff::Array,
  aff::ConstArray, aff::Series, and aff::ConstSeries expose some of their
  internals. This concerns the underlying shape as well as the represented
  data.

  aff::ConstArray and aff::ConstSeries provide a read-only reference to the
  data (i.e. an aff::ConstSharedHeap object) through their member-functions
  aff::ConstArray::representation and
  aff::ConstSeries::representation, respectively.
  In the same way aff::Array and aff::Series return an aff::SharedHeap through
  their representation member function.

  All of them return a copy of their shape through the member functions
  aff::Array::shape, aff::ConstArray::shape, aff::Series::shape, and
  aff::ConstSeries::shape, respectively. The type of the appropriate shape is
  available through a member typedef (
  see "\ref sec_design_interface_typedef").

  In return all containers provide a constructor that takes a representation
  and a shape object and checks for their consistency.

/*----------------------------------------------------------------------*/

<HR>
\section sec_design_hierarchy Class hierarchy: member data vs. inheritance

  Containers like aff::Array rely on functionality provided by other classes.
  They are based on shapes like aff::Strided and memory representations like
  aff::SharedHeap (see "\ref page_representation").

  \par An array isn't a shape. 
    Thus it would look like better design to use shapes as member data.
    We prefer, \b however, to derive privately from the shape classes. 
    This hides them from the outside (apart from explicit access - 
    see "\ref sec_design_interface_internals").
    At the same time we make use of using declarations to provide access to
    member functions like aff::Strided::size() that make also sense as a member
    of aff::Array.

  \par An array is some kind of memory representation.
    Thus it would look like proper design to derive an array from a
    representation class.
    We prefer, \b however, to use the memory representation as a private
    member. 
    We think of the representation as an individual and independent object
    that can be passed (e.g.) from an aff::Array to and aff::Series.
    Also due to the replication of the representation in aff::Array 
    (see "\ref sec_design_replicated") and the distinction between containers
    that allow data modification and containers that allow only read access
    this leads to a clearer design.
    This is reflected by the conciseness of the array constructors.
    Use the representation class as member data should introduce no runtime
    overhead. 
    The full class specification including member data is available at
    compile-time. 
    This should enable compilers to do excessive inlining.

/*----------------------------------------------------------------------*/

<HR>
\section sec_design_replicated Replicated ConstSharedHeap 

\subsection sec_design_replicated_fact Design decision
  aff::Array has a member of type aff::SharedHeap (which is exposed to the
  outside through aff::Array::representation), which itself inherits from
  aff::ConstSharedHeap. 
  At the same time aff::ConstArray has a member of type aff::Array and
  inherits itself from aff::ConstSharedHeap (which is exposed to the outside
  through aff::ConstArray::representation).
  Thus the class aff::ConstSharedHeap is replicated in aff::Array and it
  is not replicated by deriving from virtual base classes a virtual base
  class.

  The same applies to aff::Series and aff::ConstSeries.

\subsection sec_design_replicated_problem Where is the problem?
  Having an array object \c a declared
  \code aff::Array<T> a; \endcode where \c T is any type, we want to pass this
  object to a function that promises constness of the elements (see 
  "\ref sec_design_const"). The function is thus declared
  \code void func(const aff::ConstArray<T>&); \endcode
  and we want to use it like
  \code func(a) \endcode
  Consequently we must offer a way to convert an
  \code aff::Array<T>& \endcode
  to an
  \code aff::ConstArray<T>& \endcode
  implicitely.
  This is done by deriving aff::Array<T> publicly from aff::ConstArray<T>.

  The memory representation is needed by both, aff::Array<T> and its base
  class. Hence aff::ConstArray<T> has to inherit from the representation. It
  would be natural for aff::ConstArray<T> to inherit from aff::ConstSharedHeap
  only. However, since the derived aff::Array<T> needs full access to an
  aff::SharedHeap<T> (to expose the representation to the outside), we might
  tend to derive aff::ConstArray<T> from aff::SharedHeap<T> privately,
  allowing only read access and conversion to aff::ConstSharedHeap.

  Why is this a problem?
  Consider the inside of the above function. We might know, that the columns
  of the passed array contain seismogram waveforms. And we might like to
  access them in an appropriate way (i.e. through an interface that provides
  waveform operations), though just reading - not modifying - the data. Then
  we would like to code something like
  \code
  template<class T>
  void func(const aff::ConstArray<T>& a)
  {
    // cycle all seismograms
    for (Tsubscript iseis=a.f(1); iseis<=a.l(1); iseis++)
    {
      // extract shape
      aff::Strided shape(a.shape());
      // collapse to waveform iseis
      shape.collapse(1,iseis);
      // create a time series
      aff::ConstSeries<T> waveform(a.representation(),
                            shape.size(), shape.first_offset());
      // operate on time series (e.g. recursive filter)
      some_waveform_operation(waveform);
    }
  }
  \endcode

  The above example requires that we can construct an aff::ConstSeries<T> from
  an aff::ConstSharedHeap<T> (which is returned by
  aff::ConstArray::representation). The same problem appears together with
  aff::ConstArray, when creating a subarray or slice from an aff::ConstArray
  with aff::subarray or aff::slice and aff::ConstArray itself knowing nothing
  about slices, etc.

  Constructing aff::ConstArray from an aff::ConstSharedHeap sounds a natural
  operation. However, aff::ConstArray will ask for an aff::SharedHeap, if we
  derive from aff::SharedHeap (as sketched above). Conclusion: aff::ConstArray
  must use an aff::ConstSharedHeap only. At the same time we must hold
  the full aff::SharedHeap together with the aff::Array object, since this must
  return an aff::SharedHeap through aff::Array::representation to allow the
  above operation (accessing data through aff::Series or constructing a
  slice - see "\ref sec_design_interface_sparse").

\subsection sec_design_replicated_solution Solution
  The most convincing solution (IMHO) to this problem is to use an
  (additional) member of type aff::SharedHeap<T> in aff::Array<T> which
  derives aff::ConstArray<T>.
  In consequence aff::ConstSharedHeap<T> is then a replicated within
  aff::Array<T>. For a proper design we might consider to make
  aff::ConstSharedHeap a virtual base, thus avoiding member data duplication.
  This would, however, introduce an extra level of indirection (additional to
  the indirection when accessing the heap data through the pointer to the
  aff::util::SHeap struct in aff::ConstSharedHeap). On the other hand, fully
  replicating the base aff::ConstSharedHeap just adds one member data pointer
  (the pointer to the aff::util::SHeap struct) to the data block in aff::Array
  (which already contains many bytes from the aff::Strided base). This
  overhead is not considered significant. 

  \b But \b notice: We now must take care to synchronize the aff::SharedHeap
  base of aff::Array and the aff::ConstSharedHeap base of aff::ConstArray
  during construction. This is no major concern, but it is error-prone to some
  degree. It is, however, much easier to keep them synchronous when using
  member data instead if inheritance.

/*----------------------------------------------------------------------*/

<HR>
\section sec_design_copy Copy constructor and copy operator
  
  Usually we would expect the copy operator and the copy constructor to have
  the same semantics. Here the copy constructor of aff::Array must have
  reference semantics (it does a shallow copy). This is necessary to allow
  arrays as return values from functions. In this case the copy constructor is
  automatically invoked. Reference semantics ensure a minimal overhead. in
  terms of memory usage and execution time.

  In the case of the copy (assignment) operator things are less clear: 
  If we define the
  copy operator to have reference semantics, it has the same behaviour as the
  copy constructor. That is what we usually would expect. An expression like
  \code
  A=B;
  \endcode
  means that array \c A drops its reference to the memory location it was
  pointing to and forgets its previous shape. Following this statement array
  \c A will refer to the same memory location as array \c B and will have the
  same shape. Both are indistinguishable.

  However, in many cases (most cases?) we will use the copy (assignment)
  operator in the
  sense of a mathematical equation. This may read like
  \code
  A=B+C;
  \endcode
  although expressions like this are not yet supported by the library
  features. In this case we do not mean that \c A should drop it reference. 
  \c A may refer to an array in memory which is also referred by other array
  instances. And we want these values to be set to the result of the operation
  \c B + \c C. In that case the copy operator should have deep copy semantics.

  \par Design decision
  The classes aff::Array and aff::Series provide copy (assignment) operators
  with shallow copy semantics. 
  The automatically created copy constructor and copy operator do just right
  for this.
  This is sensible, because we are not offering mathematical array operations.
  This operations may be delegated to a wrapper class in the future, which
  then also may provide expression templates and an appropriate assignment
  operator.

/*----------------------------------------------------------------------*/

<HR>
\section sec_design_namespaces Namespaces

  We group all code in two namespaces. Major modules which will be accessed by
  the user are placed in namepsace aff. Modules meant to be used internally are
  placed in aff::util.
  Use directives like
  \code
  using namespace aff;
  \endcode
  or
  \code
  using aff::Array;
  \endcode
  for convenient access.

/*----------------------------------------------------------------------*/

<HR>
\section sec_design_binary Binary library

  We provide a binary version of the library. It contains a set of prebuilt
  class objects. Using this version and linking against the binary library
  libaff.a should reduce compilation times in comparison to complete
  template evaluation.
  This will become more significant the more code is factored out to separate
  definition headers.
  This approach offers no improvement with inlined code (which we use
  extensively in array access functions).

  To use the binary version you should include binarry.h in place of array.h
  You will find modules aff::Array and aff::SharedHeap
  in aff::prebuilt that are in aff in the full-template version.

  \sa tests/binarraytest.cc
  \sa binarray.h

  The inclusion of header files is controlled by a set of preprocessor macros.
  \sa AFF_PREBUILT
  \sa AFF_INDEXCHECK
  \sa AFF_NO_DEFINITIONS
  \sa AFF_COMPILING_LIBRARY
  \sa DOXYGEN_MUST_SKIP_THIS

\note
Since we reduced to number of template parameters significantly in this
approach, many parts of code have already been factored out to separate files
that are compiled into the binary libaff.a. The approach of explicitly
instantiated class templates is not supported so far. It is, however, prepared
in the structure of header files and may be activated in the future.
\date 20/12/2002

/*----------------------------------------------------------------------*/

<HR>
\section sec_design_multidimensional Multidimensional arrays

  \todo
  Explain Wolfgangs idea of multidimensional arrays.

/*----------------------------------------------------------------------*/

<HR>
\section sec_design_const Notes on the const-correctness of arrays

\subsection sec_design_const_problem Where is the problem?
  When passing a container (i.e. an array) to a function, we would like to
  promise that the values in the container are not modified, in case the
  function uses only read-access. Consider a declaration
  \code void func(const int& v) \endcode
  of a function that takes and argument of type \c int an promises that this
  will not be modified. Passing by reference is used, because this is more
  efficient than passing by value (in particular for large objects - which is
  not the case for \c int, but for an array).
  And qualifying the type \c const promises that the
  value passed by reference will not be changed.

  A declaration
  \code void func(const Array<int>& v) \endcode
  does not what we want (see "\ref sec_design_const_general"). It just
  promises the constness of the container, not of the data. Within the
  function the passed reference may be assigned to a non-const \c Array<int>,
  which allows modification of the data (see "\ref page_representation").

  Thus we must use something like
  \code void func(const ConstArray<int>& v) \endcode
  where \c ConstArray<int> does not allow modification of the data (be no
  means - copying and conversions included) and may be derived from an 
  \c Array<int> by a trivial conversion (like a conversion to a public base
  class).

\subsection sec_design_const_approach The approach used in this library

  We distinguish between the constness of the array and the constness of the
  elements. A definition
  \code
  aff::Array<int> A(12,12);
  const aff::Array<int> B(A);
  \endcode
  means that array \c B is a constant array initialized to array \c A. This
  means, that the container is constant. Its shape and reference may not be
  changed.

  If you want to define constness of the contained values (e.g. when passing
  an array to a function), you have to use
  \code
  aff::ConstArray<int> C(A);
  \endcode
  which defines that the contents of \c C may not be changed (i.e. they are of
  type \c const \c int. 
  They are still refering to the same data in memory. 
  If you modify data elements through \c A, this will be visible through \c C.

  An array for elements of type \c T is derived from an array for elements of
  type \c const \c T. 
  Functions that only need read access to arrays should be declared like
  \code
  void func(const aff::ConstArray<int>& array);
  \endcode
  and may be called like
  \code
  aff::Array<int> A(12,12);
  func(A);
  \endcode
  The type conversion from \code aff::Array<int> \endcode to 
  \code const aff::ConstArray<int>& \endcode is trivial and has no runtime
  overhead.

  Each container class must deal with this issue on its own. Sorry...

  \sa aff::ConstSharedHeap
  \sa aff::ConstArray
  \sa aff::ConstSeries

\par Restrictions for containers with const qualifier
  Strictly distinguishing between constness of the container and constness of
  the contained data would allow to modify data through an object \c c that
  was declared
  \code const Array<int> c; \endcode
  The containers in this library (aff::Array, etc.), however, provide only a
  reduced set of access operators, when declared with \c const qualifier.
  They do not allow direct modification of the data (only through assignment
  to a non-const container instance).
  Although the constness of the container object generally does not imply
  constness of the contained data, we think that every user will expect the
  classes to behave like this.
  To ensure true constness of the data, you have to assign to the base class
  of the container. 
  Any container class (e.g. \c Cont) provides the type of container for const
  elements through a typedef Tcontainer_of_const 
  (i.e. \c Cont::Tcontainer_of_const) or short Tcoc.
  Remember that a \c const \c aff::Array always
  may be assigned to a mutable aff::Array, which in turn allows modification
  of the data!

\subsection sec_design_const_alternatives Alternatives

  Three alternatives to this concept have been discussed (and discarded).
  Both have the appealing property of needing only one class definition for
  each container (in contrast to a class and a base class in our case).
  Additionally both would offer name commonality for containers of non-const
  elements and containers of const elements.

\par Using arrays with element type const T
  A rather straight approach is to use the element type \c const \c T
  where an array of elements of type \c T should be used, that we do not allow
  to be changed. This design concept can be accomplished with a special traits
  class that is specialized for \c const \c T and allows to derive a mutable
  or const version of any type. Be further providing appropriate conversion
  operators, an \code Array<T> \endcode could be converted to an
  \code Array<const T>, \endcode both sharing the same elements in memory.
  In this approach, however, both container classes are completely
  independent (although having the same name) due to their different template
  arguments. The conversion to the container for const elements is not a
  trivial conversion (like for a reference to a reference of a public base
  class) and must be done explicitely. That's inconvenient for the most common
  use (i.e. passing a container to a function).

\par Deriving from a template specialization
  The name commonality could still be achieved by deriving the Array<T> from
  template specialization Array<const T>. In this case the specialization must
  be used as a base class before it is actually defined. That's impropoer
  design.

\par Ensuring constness of elements through const qualifier of functions
  We could strictly follow the concept (as we do anyway to some extent) to
  couple the constness of the container to the constness of the contained
  data. This is done by const qualifiers to member functions that allow
  modification of the data. Avoid pitfalls, we have to consider copy operators
  and copy constructors then too. Both must not promise const-ness to their
  arguments. While this works in principle, we would end up with a container
  class which doesn't allow copies of const instances. Hence we could not
  return a container from a function, that ensures that the accessed data
  cannot be modified.

\subsection sec_design_const_general General considerations

  Arrays using the shared heap representation have reference semantics.
  Different instances will access the same data in memory. Copying an array
  instance just copies a reference to the data. This mechanism is not obvious
  to the compiler. The array instances are values in the sense of C++ types
  and not references. Passing an \c const \c aff::Array to a function does
  not prohibit the function from assigning this instance to a non-const
  \c aff::Array, which then references the same memory area and allows the
  modification of the values contained in the array.

  Generally it has to be defined, what is meant by declaring an array instance
  to be \c const. In the first place this means constness of the container to
  the compiler. The compiler will ensure, that the container (array class) is
  not changed, thus no data member of the array is changed. This means that
  the array will keep the reference to the same data and that the
  index-mapping defined by the array shape may not be changed. However, the
  compiler will not prevent to change any data, the array refers to. 

  We may define access operators that have a non-const version that returns a
  reference to the data, allowing to change the data values together with a
  const version that returns a value of const reference, thus preventing the
  data from being changed through an instance that is declared const. However,
  the compiler will always allow to create a non-const copy of a const array
  instance. In the sense of const-ness of C++ data, this does not violate the
  const-ness of the source of the copy. The shape of the original array may
  not be changed. Only the shape of the copy may be changed. But the data of
  the original array may now be changed through the copied instance, since our
  array classes implicitly have reference semantic. Thus we have to
  distinguish between const-ness of the container (array class instance) and
  the contained data (values in memory the arrays refers to).

  In this library we will not provide a const and a non-const version of the
  array classes. With templated code it is more convenient to use an array
  with element type \c const \c T as the const version of an array with
  element type \c T. To allow conversion of an instance with element type \c T
  to an instance of type \c const \c T, we use the version for elements of
  type \c const \c T as a base classe.

   -  The need of const-correctness is discussed in "Chapter 1 Introduction,
      C++ Conventions, Implementation of Vector and Matrix Classes" of
      "Numerical Recipes in C++". A link to a PDF file of this chapter is
      provided at "http://www.nr.com/cpp-blurb.html".
   - The "C++ FAQ Lite" discusses many aspects of const-correctness in Chapter
     18, which you find at
     "http://www.inf.uni-konstanz.de/~kuehl/cpp/cppfaq.htm/const-correctness.html".
   -  You may find my thoughts about const-correctness with containers that
      have reference semantics at
      "http://www.geophysik.uni-frankfurt.de/~forbrig/txt/cxx/tutorial/consthandle.doc/doc/html/index.html".

*/

/*======================================================================*/

/*! \page page_using HOWTO use this library

  Contents of this page:
  - \ref sec_using_constructor
  - \ref sec_using_examples

\section sec_using_constructor Constructing arrays
  Arrays are most easy constructed by means of the aff::Shaper.
  If you want e.g. define an array \c A of element type int with Fortran
  layout, three dimensions and the index ranges [-2:2], [1:4], and [6:10] you
  have to code
  \code
  using namespace aff;
  Array<int> A(Shaper(-2,2)(4)(6,10));
  \endcode
  The shaper is presented in aff/shaper.h.

\section sec_using_examples Example code
  The test programs may serve as examples for using this library:
  - tests/arraytest.cc
  - tests/shapetest.cc
  - tests/reprtest.cc
  - tests/simplearraytest.cc

\todo
We need more text and examples.

*/


/*======================================================================*/

/*! \page page_notes General notes

  Contents of this page:
  - \ref sec_notes_need

\section sec_notes_need The need of an array library
  
  One major reason for replacing Fortran77 by C++ in numerical code is the
  convenience in expressing logistics. Data of different type and size may be
  packed into classes and encapsulated from the outside world. Most numerical
  results are to be stored in arrays, multi-dimensional arrays in particular.
  This library provides the basic functionality for storing many data of the
  same type in memory, passing them around between subroutines in an efficient
  way and accessing them through convenient interfaces. The main purpose of
  this library is not calculation but managing (passing between program
  modules, selection of subsets of the data) large amounts of numbers. In the
  future it might provide interfaces to libraries like blitz++ for finite
  difference calculations, MTL for linear algebra calculations, and POOMA for
  parallel computations.

*/

/*======================================================================*/

/*! \page page_naming Naming conventions

  Contents of this page:
  - \ref sec_naming_identifiers
  - \ref sec_naming_macros
  - \ref sec_naming_files

\section sec_naming_identifiers Classes, Typedefs, etc.

  During coding it is sometimes helpfull to recognize the meaning of an
  identifier due to some signals in irs name. Therefor the following
  guidelines are used. The nameing of template parameters is left free for
  convenience.

  \par Classes
   
  Class names always start with a capital letter.

  \par Typedefs

  Typedefs always start with a capital \c T.

  \par Member data

  Member data identifiers always start with a capital \c M.

\section sec_naming_macros Preprocessor macros

  Preprocessor macros like include-guards should have the prefix "AFF_".
  The macros in the \ref group_helpers are an exception to this rule.

\section sec_naming_files Filenames

  Files with the extension \c .cc contain only non-template definitions. Files
  with the extension \c .h may contain prototypes, class declarations or
  template code. Files ending on \c def.h contain template code definitions
  that is factored out to be compilable into a binary library for explicit
  instantiation.

  The main directory %aff contains headers that are usually included by the
  user. A subdirectory %aff/lib contains additional headers that are mostly
  used internally.

*/

// ----- END OF README -----