J3/03-260
Date: 20 October 2003
To: J3
From: Aleksandar Donev
Subject: Post Fortran 2003: Genericity in Fortran
This is a proposal for a feature to be provided in some future version of
Fortran.
______________________________________
Summary
______________________________________
I first review the Basic Functionality that this proposal addresses. I give 4
problems which could elegantly and efficiently be solved with this proposal,
and discuss them in detail in the Motivation. I first digress to describe
what is in other programming languages, and give basic terminology in the
Background section.
Although I try to describe things from scratch, I will assume some familiarity
with macros (with parameters) and/or C++ templates and/or Ada generic
packages and/or Eiffel generic classes.
______________________________________
Basic Functionality
______________________________________
Generic code is one which applies to a variety of specific types and/or type
parameters. Fortran has a little bit of genericity in it due to generic
*interfaces* and parameterized types. However, what is lacking is the ability
to write the *body* of the procedures which enter in the generic interfaces
or operate on objects of parameterized type. In most cases this body is
independent of the actual type and type parameters of the generic resolution
parameters.
This proposal is concerned with additions to Fortran to enable one, some or
all of the following basic tasks, *avoiding* needless repetition of code and
still providing *maximal* efficiency (such as inlined code):
Task 1) Write a module with a parameterized derived type and associated
procedures which work for any kind parameter.
Task 2) Write a generic procedure like the intrinsic MAXVAL purely in Fortran.
Task 3) Write a module which provides generic data-structures such as a
generic stack.
Task 4) Write a generic procedure which can sort an array of arbitrary type.
These tasks are ordered in what I consider to be increasing complexity in
terms of decisions to make and also incorporating into the standard
(complexity of description). I will discuss implementation separately, and
believe that all of these can be implemented with minimal effort, but a
"quality implementation" might require more effort.
______________________________________
Rationale
______________________________________
I believe the ability to do tasks 1 and 2 need to be in the next revision of
Fortran. Almost any user other then the basic beginner will benefit from this
and without it the full power of Fortran generics and parameterized types
cannot be realized and will not be used widely. Tasks 3 and 4 are more
ambitious, and may be less-widely used, but should be considered by the
committee carefully.
Most of these can already be done using:
a) Cut and Paste and endless repetition of code. This is very error prone and
wastes programmer's effort and time. Sometimes INCLUDE files are used to
avoid some repetition.
c) Macros, such as CoCo/m4/FWEB etc. and include files. This is not only
non-standard, but difficult for the nonexpert, and is also error prone, as
discussed later.
I propose that basic Fortran provide this functionality, to do away with the
need to distribute things like Perl scripts or macro languages with Fortran
libraries.
______________________________________
Background
______________________________________
Genericity means the ability to write code that applies to multiple specific
types, i.e. specification *and* executable code that is parameterized by a
certain (possibly parameterized) type T and/or an (integer) type parameter K.
I will call T the generic type parameter and K the generic kind parameter.
Genericity is closely related to inheritance, however, I want to stress that
it is in fact *complementary* to it, and I hope to illustrate this here. The
main difference is that generic code, as I consider it here, *cannot* be
compiled until the exact type T and kind K are known, whereas code using
inheritance and related concepts like polymorphism, is compiled only once and
then it works for multiple types using "type descriptors" in the runtime
implementation. The key is that polymorphism uses pointers to avoid knowing
the exact type of an object. This has a significant run time cost, like
dynamic dispatch, memory indirection, aliasing, etc. Genericity on the other
hand will enable us to avoid all of this and even enable inlining of the
generic code.
The reader familiar with macros can think of generic code as a kind of macro
for generating specific code (meaning code for a specific T and K) that is
then actually compiled. However, I am not describing or proposing a
Fortran-aware macro system in this proposal! The relation between macros and
generic code is like that of macro constants (#define's) and Fortran
PARAMETERs. The former provide the functionality of Fortran constants, but
without the appropriate scoping or type-checking abilities. Basically this
whole proposal is about making certain kind of macros statically typed and
endowing them with a Fortran scope.
In this sense, the generic code is the macro, or template (C++ terminology).
When this macro is used (with specific T and K), the compiler compiles, or
instantiates (C++ terminology) the code for specific T and K. The last step,
which I will call instantiation, is unavoidable, since T and K must be known
before executable object code can be produced. However, whether the generic
code itself can be "compiled" is the main source of dilemma which I address
here.
There are 3 main kinds of genericity, as found in different languages:
____________
A) Unlimited Unconstrained Genericity (UUG):
____________
This is basically what is provided by C++ templates, and it means that there
is *no* restriction on the type T (the kind parameter K is a uniquely Fortran
thing). Templates basically provide macros with basic language awareness,
such as syntax awareness (balancing braces and parenthesis, for example) and
scope. They do *not* provide any type checking.
To illustrate this, here is a C++ function template for a function which
returns the smaller of two values:
template T minimum(T A, T B)
{
if(A**;
function minimum(x,y: T) return T is
begin
if x {
public boolean gt (A that);
}
class SortedObjects> {
public A minimum (A first, A second) {
if(first.gt(second))
return second
else
return first
}
This background illustrates the kind of decisions that need to be made when
implementing genericity in a statically typed language. I next tackle several
typical Fortran programming tasks that are best done using genericity.
______________________________________
Motivation/Examples
______________________________________
Here I discuss one by one the 4 tasks given in the Basic Functionality. I
propose solutions but also raise what problems/questions remain.
____________
Parameterized Types and their Operations
____________
Take the following parameterized type which defines a point in 3D space whose
position is stored using single or double precision reals, and one type bound
procedure which translates the point:
INTEGER, PARAMETER :: r_sp=KIND(1.0E0), r_dp=KIND(1.0D0)
! Single and double precision real kinds
TYPE :: Euclidian_Point(KIND)
INTEGER, KIND :: KIND
REAL(KIND) :: position(3)
CONTAINS
GENERIC, PASS(point) :: Translate=>Translate_sp, Translate_dp
END TYPE Euclidian_Point
and we have:
SUBROUTINE Translate_sp(point, translation)
CLASS(Euclidian_Point(r_sp)), INTENT(INOUT) :: point
REAL(KIND=r_sp) :: translation(3)
point%position = point%position + translation
END SUBROUTINE
SUBROUTINE Translate_dp(point, translation)
CLASS(Euclidian_Point(r_dp)), INTENT(INOUT) :: point
REAL(KIND=r_dp) :: translation(3)
point%position = point%position + translation
END SUBROUTINE
Notice how the single and double precision versions of Translate are identical
save for the kind-type parameter, r_sp in one, r_dp in the other. This is
needless repetition of code. Furthermore, if later the compiler is extended
to provide quadrupole precision, one needs to go back and add yet another
duplicate version of Translate. Clearly this is undesirable. For all the
extensibility/reusability we have provided with inheritance we have forced
the programmer to duplicate code and also fix the future usage at the design
stage.
Instead, one should be able to write something like (this is ficticious
syntax):
TYPE :: Euclidian_Point(K)
INTEGER, KIND :: K
REAL(KIND=K) :: position(3)
CONTAINS
GENERIC, PASS(point) :: Translate
END TYPE Euclidian_Point
GENERIC SUBROUTINE Translate(point, translation)
CLASS(Euclidian_Point(KIND=*)), INTENT(INOUT) :: point
! Works for any KIND (the kind is "assumed")
REAL(KIND=point%K) :: translation(3)
point%position = point%position + translation
END SUBROUTINE
and simply use this:
TYPE(Euclidian_Point(r_sp)) :: point
CALL point.Translate((/1.0_r_sp,1.0_r_sp,1.0_r_sp/))
Full type-safety has been preserved and the simplification and ease is
amazing! This is what genericity should look like in Fortran!
How will the compiler do this? There are two options:
1) When the compiler compiles the programming unit containing the procedure
Translate, it will compile a separate version for each type of real it
supports, and also decorate the procedure names itself. It is exactly what
the user has to do manually today by replicating code and changing an sp into
a dp.
2) The compiler waits until it compiles the code that uses a
Euclidian_Point(r_sp) and then it compiles a specific version of Translate
for single precision reals.
In this case strategy 1 clearly seems preferable. The problem is the
following: What if there are 3 different kind parameters, and 3 possible
values for each. Does the compiler compile all 27 versions of the generic
procedure? Furthermore, what if the compiler does not know what the possible
values for K are? For example, what if I wanted to provide points in both 2
and 3 dimensions using another kind parameter DIM:
TYPE :: Euclidian_Point(K, DIM)
INTEGER, KIND :: K, DIM
REAL(KIND=K), DIMENSION(DIM) :: position
CONTAINS
GENERIC, PASS(point) :: Translate
END TYPE Euclidian_Point
The compiler does not know that I will only use points in 2 and 3D (i.e. DIM=2
and DIM=3). So how do I tell it that?
The basic gist of this example is that the type T is fixed (in this case to
Euclidian_Point), and only the type parameter K is varied. Next we want to
get more demanding and ask that the type T also be allowed to change, but we
can predict a-priori what (intrinsic) types T we want to use.
____________
A generic procedure for all supported REALs and COMPLEX
____________
In the first section I mentioned as an example writing something like the
intrinsic MAXVAL in Fortran, without repetition of code. A more realistic
example is writing something like the level-I BLAS in pure Fortran. The BLAS
works for several different kinds of REALs and also COMPLEX numbers, and in
level-I we have things like AXPY:
y=a*x+b*y
where x and y are arrays and a and b are scalars. As an illustration assume
that we want to code a generic function Add which adds two vectors (rank-1
arrays) of different kinds of REAL or COMPLEX numbers. Here is how a possible
generic Fortran code to do this might look:
MODULE BLAS_1
! Implements an Add operation on two vectors
! Imagine this being an implementation of Level 1 BLAS
! for all kinds of real/complex supported on a platform
IMPLICIT NONE
PRIVATE
PUBLIC :: Add
CONTAINS
GENERIC FUNCTION Add(x,y) RESULT(x_plus_y)
TYPE(REAL(*),COMPLEX(*)), DIMENSION(:), INTENT(IN) :: x,y
! x and y can be any kind of REAL or COMPLEX
! But they must both be of the same type/parameter
TYPE(TYPE_OF(x)), DIMENSION(SIZE(x)) :: x_plus_y
! Must be the same type/parameter as x
x_plus_y=x+y
END FUNCTION Add
END MODULE
which means exactly the same as if one used macros to generate:
MODULE BLAS_1
IMPLICIT NONE
PRIVATE
PUBLIC :: Add
INTERFACE Add
MODULE PROCEDURE Add_real_sp
MODULE PROCEDURE Add_complex_sp
...! All other supported precisions
END INTERFACE
CONTAINS
FUNCTION Add_real_sp(x,y) RESULT(x_plus_y)
REAL(r_sp), DIMENSION(:), INTENT(IN) :: x,y
REAL(r_sp), DIMENSION(SIZE(x)) :: x_plus_y
! Must be the same type/parameter as x
x_plus_y=x+y
END FUNCTION
FUNCTION Add_complex_sp(x,y) RESULT(x_plus_y)
COMPLEX(r_sp), DIMENSION(:), INTENT(IN) :: x,y
COMPLEX(r_sp), DIMENSION(SIZE(x)) :: x_plus_y
! Must be the same type/parameter as x
x_plus_y=x+y
END FUNCTION
...
END MODULE
The proposed syntax above is not one that I actually like, but rather an
illustration. The point is that we know that the given generic code, in this
case the generic procedure Add, is to be used with only a certain
*predefined* set of types and type parameters, and therefore everything can
be precompiled and type-safety is ensured. I am leaving details about the
syntax aside for now. This also fits very well into the Fortran framework.
Namely, standard Fortran already provides such generic procedures for the
intrinsic types, for example, SUM or MINVAL. But the user cannot extend the
system by writing his own generic procedures like SUM or MINVAL easily, or
writing SUM for his own (parameterized) derived types, such as, for example,
rational numbers (of single, double, quad, etc. precision) or
arbitrary-precision floating-point numbers, without using excessive code
duplication.
So far I have illustrated that there are two "noncontroversial" cases where
genericity is needed, and these are already widely seen used among Fortran
programmers (where cut/paste, macros, perl scrips, and other wizzardry is
used to generate the body of the procedures above):
1) When only a kind parameter changes and the type is fixed.
2) When the type also changes but the set of types is known a-priori.
Both 1 and 2 are easy to compile if the set of kind parameters is also fixed,
especially if it can be determined by the compiler. Namely, the compiler can
just precompile all possible combinations of types/type-parameters.
The above system maintains a clear separation between types, which we can
already parameterize with integers, and procedures, which I propose we allow
to be parameterized by integers and also work on several different types. I
believe it is better to design a system which unifies both and allows one to
parameterize a whole "package", i.e. a collection of type definitions,
constants and procedures which operate on those types and use those
constants. I will later give examples which invent a new GENERIC programming
unit which does this.
____________
Generic Stack
____________
As I said above, Fortran already has built-in intrinsic procedures which work
with, for example, any numeric (REAL, COMPLEX or INTEGER) type, like SUM. I
discussed in the previous two examples how we can allow the user to write
such procedures him/herself.
But Fortran also has intrinsics which work with *any* type. For example,
CSHIFT will shift an array of any type. Can we allow the user to write code
which works efficiently for any type (and yet does not use CLASS(*) pointers)
and is this useful in real-life applications? I believe the answer is a big
YES on both accounts and discuss an example next.
To illustrate how one can provide unconstrained limited genericity which works
on any type and yet is completely statically typed and checkable at compile
type, I will use a generic stack as an example. This would be a typical kind
of thing found in the widely used Standard Template Library in C++. One can
already do "generic" stacks in Fortran using polymorphic (CLASS(*)
especially) pointers. By using generic code one can avoid always having to
drag pointers into this, and implement a generic stack using a simple array,
just as if one were writing a stack of integers or reals. The example code
below uses no pointers or dynamic dispatch, and is maximally efficient and
very easy to write/use.
In this example I introduce a new programming unit, I call it GENERIC, which
contains type definitions and procedures parameterized by an arbitrary type
any_type, which must be a specific type, i.e., have all its type parameters
specified:
module GenericStacks
generic :: GenericStack(any_type)
! This can be used with *any type*, there are *no* requirements
what-so-ever
private
type, public :: generic_stack
public
integer :: n_elements=0, n_max_elements=100
type(any_type), allocatable, dimension(:), private :: storage
contains
public
procedure, pass(stack) :: initialize, pop
...
end type
contains
subroutine initialize(stack)
class(generic_stack), intent(inout) :: stack
allocate(storage(n_max_elements))
! No need for SOURCE or MOLD here
end subroutine initialize
function pop(stack) result(top)
class(generic_stack), intent(inout) :: stack
type(any_type) :: top ! No POINTER needed here
if(n_elements<=0) return
top=storage[n_elements]
n_elements=n_elements-1
end function
...
end generic
end module
Now, the generic GenericStack cannot really be compiled until the type
any_type is known. To use a generic stack, one must specifically instantiate
the generic with a specific type. This instance can be given a name and
notation similar to type selection used to refer to the specific types and
procedures it defines:
program RealStacks
use GenericStacks
generic(GenericStack(real(kind(0.0)))) :: real_stack
! Now actually compile the code
! to get a generic stack of single-precision reals
type(real_stack%generic_stack) :: stack
! Declare a stack of reals
! Now use this stack:
call stack.initialize()
! Or "call real_stack%initialize(stack)"
...
write(*,*) "Top element is:", stack.pop()
end program RealStacks
What exactly can go inside a GENERIC block parameterized by a type T. Well,
anything which according to the current standard works no matter what the
type T is. For example, if inside the GENERIC we have:
type(T), target :: x
type(T), pointer :: y
type(T), dimension(:), target :: z
type(c_ptr) :: p
then any of these are OK:
allocate(z(5))
y=>x
z(5)=x
p=C_LOC(x)
etc.
We may need to add words in certain places of the standard to explicitly allow
this (like in allocate statement), but in many cases we do not make any
specific requirement on the type of x or y, or only make a requirement about
the relative type of x and y (for example, y must be type-compatible with x),
and these are clearly satisfied by the examples above.
I also believe we should allow the type T to be used in a SELECT TYPE
construct:
SELECT TYPE(T)
CASE (INTEGER(sp))
WRITE(*,*) "Stack of integers"
CASE DEFAULT
WRITE(*,*) "Stack of something???"
END SELECT TYPE
and/or allow one to call a procedure whose dummy is declared to be of CLASS(*)
with an actual whose type is the generic type parameter T. In C++
terminology, this is related to the concept of "specialization". Namely,
though most generic code is completely type-independent, there may be small
pieces of code where it is necessary to be more specific. An example is
writing a set of Fortran-friendly wrappers to, for example, the Mpi_Allgather
function in the MPI C Binding. The C prototype here is:
int MPI_Allgather(void* sendbuf, int sendcount, MPI_Datatype sendtype, void*
recvbuf, \
int recvcount, MPI_Datatype recvtype, MPI_Comm comm)
and we would like to write a Fortran wrapper which avoids the need to pass the
type (especially if there is a predefined MPI datatype for the given type--I
use SELECT TYPE for this below) and number of elements twice and is more
strongly typed, namely, the send and receive buffer must of the same type.
Most Fortran programmers would prefer such an interface because it avoids
having to deal with C directly:
MODULE MPI_Interface
USE ISO_C_INTEROP
USE MPI_DATATYPES ! Assume there is a vendor MPI module somewhere
PRIVATE
PUBLIC :: MPI_Gather ! A generic interface for a wrapper around MPI
INTERFACE
FUNCTION MPI_Allgather_C(sendbuf,sendcount,sendtype, &
recvbuf,recvcount,recvtype,comm) &
BIND(C,NAME="MPI_Allgather") RESULT(status)
TYPE(C_PTR), INTENT(IN), VALUE :: sendbuf,recvbuf
INTEGER(C_INT), VALUE :: sendcount, recvcount
TYPE(MPI_Datatype), VALUE :: sendtype, recvtype
TYPE(MPI_Comm), VALUE :: comm
INTEGER(C_INT) :: status
END FUNCTION
END INTERFACE
GENERIC, PUBLIC :: MPI_Gather(any_type)
PUBLIC :: MPI_ALLGATHER
CONTAINS
SUBROUTINE
MPI_ALLGATHER(sendbuf,recvbuf,data_count,data_type,comm,status)
TYPE(any_type), DIMENSION(*), INTENT(IN), TARGET :: sendbuf
TYPE(any_type), DIMENSION(*), INTENT(OUT), TARGET :: recvbuf
INTEGER(C_INT), INTENT(IN) :: data_count
TYPE(MPI_Datatype), INTENT(IN), OPTIONAL :: data_type
TYPE(MPI_Comm), INTENT(IN) :: comm
INTEGER(C_INT), INTENT(OUT), OPTIONAL :: status
INTEGER(C_INT) :: error_status
TYPE(MPI_Datatype) :: mpi_type
SELECT TYPE(sendbuf)
! There are some predefined types in MPI
! For these types we don't need data_type
TYPE IS(C_INT)
mpi_type=MPI_INT
TYPE IS(C_FLOAT)
mpi_type=MPI_FLOAT
...
CLASS DEFAULT
! This is not a predefined type
IF(PRESENT(data_type)) THEN @;
mpi_type=data_type
ELSE
mpi_type=MPI_PACKED
END IF
END SELECT TYPE
// Now actually call the C subroutine
CALL MPI_Allgather_C(sendbuf=C_LOC(sendbuf), sendcount=data_count, &
sendtype=mpi_type, recvbuf=C_LOC(recvbuf), recvcount=data_count, &
recvtype=mpi_type, comm=comm)
END SUBROUTINE
END GENERIC MPI_Gather
! We can now compile specific instances for several common types:
GENERIC(MPI_Gather(INTEGER)) :: gather_i_sp
! Integer version
GENERIC(MPI_Gather(REAL(KIND(0.0))) :: gather_r_sp
! Single-precision reals
GENERIC(MPI_Gather(REAL(KIND(0.0))) :: gather_r_dp
! Double-precision reals
...
! And finally we can put these in a generic
INTERFACE MPI_Gather
PROCEDURE :: gather_i_sp%MPI_ALLGATHER, &
gather_r_sp%MPI_ALLGATHER, gather_r_dp%MPI_ALLGATHER
END INTERFACE
END MODULE
____________
Procedures which work on some unknown type
____________
We now come to the most difficult and controversial case. This is when the
type T and the operations appearing inside the generic code are not
restricted. The main characteristic of such a case is that the syntax cannot
be fully verified, i.e., although the syntax can be parsed, the meaning of
the syntax is not clear at the point when the generic code is written. Take
the simple example of a sorting routine for objects of an arbitrary type T.
Any sorting routine would have to compare two quantities of this type, so
inside the generic code there might be something like:
GENERIC QuickSort(T)
...
TYPE(T), ... :: A, B
IF(A****y
is legal if the type of x is the same as the type of y. Never is there any
restriction on what this type has to be. So there is absolutely nothing to be
changed if we allow the type of x and y to be parameterized by some type T.
The only thing we need to change is the restriction which says that x and y
have to be declared to have some intrinsic or accessible derived type.
In any case, I do not think it is hard to incorporate the simpler forms of
genericity in the language. As far as implementation goes, they are all
almost trivial to implement---simply use a macro-type expansion mechanism. Of
course, a quality implementation may do better. The point of genericity is
that real code (i.e. code to be optimized into object code) is obtained only
once a specific type is chosen for the type parameter T, and this code is
simply plain-old Fortran. Therefore only small modifications to the front-end
of compilers are needed in order to parse the generic code blocks and
generate the appropriate intermediate representations for the specific
type(s) T that are used. Optimizers or back-ends are not affected at all.
______________________________________
Detailed Specification
______________________________________
As can be seen above, there are many choices to be made before more detailed
specifications can be provided. The main decision is to decide what kinds of
genericity we want to provide in Fortran:
1. Allow for an "assumed" kind parameter for dummy arguments in procedures
(first example above):
TYPE(INTEGER(KIND=*)) :: x
TYPE(INTEGER(x%kind)) :: y
2. Allow for the type of a dummy argument to be a set of types, rather then a
single type (second example above):
TYPE(INTEGER, REAL), INTENT(IN) :: x
TYPE(TYPE_OF(x)) :: y
3. Combined 1 and 2 above, i.e. allow for things like:
TYPE(INTEGER(*), REAL(*)) :: x
TYPE(TYPE_OF(x)) :: y
4. Allow the type of a variable to be some arbitrary type T, but only allow
operations on that variable which are valid for any type T:
GENERIC Test(T)
TYPE(T) :: x,y
x=y
...
END GENERIC
5. Allow for unlimited unconstrained genericity, as in C++ templates.
I would say all five are useful, and would vote for 1-4 to be incorporated
into the next revision of Fortran. I hope I have explained above in what
kinds of situations different kinds of genericity are needed. Certainly just
choice 4 above is not enough. Choice 1 above is IMO a non-brainer and it is
high-time we provide this in Fortran. I also think choice 2 is useful and not
so controversial or complicated, and choice 3 is a logical combination of 1
and 2.
! EOF
_________________________________
Aleksandar Donev
Complex Materials Theory Group (http://cherrypit.princeton.edu/)
Princeton Materials Institute &
Program in Applied and Computational Mathematics
@ Princeton University
Address:
419 Bowen Hall, 70 Prospect Avenue
Princeton University
Princeton, NJ 08540-5211
E-mail: adonev@math.princeton.edu
WWW: http://atom.princeton.edu/donev
Phone: (609) 258-2775
Fax: (609) 258-1177
__________________________________
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