As an illustration, we will consider a program which calculates properties of a cube. Some of the properties depend on the edge length of the cube, some others depend on the Cartesian coordinates of the vertices.

## The Implicit Reference to Parameters method

In scientific programming, a program can almost always be seen as a pure function of its data:

output = program(input)


In this functional view, a program can be represented as an acyclic graph, where:

• the vertices of the graph are the entities of interest
• the edges of the graph represent the relation {needs/needed by}

We call this graph the production tree.

Consider the example of the electronic energy of a molecular system:

$$E = E_{\text{nucl}} + E_{\text{elec}}$$

decomposed as the nuclear repulsion energy and the electronic energy. The electronic energy can be expressed as the sum of the potential and kinetic electronic energies:

$$E_{\text{elec}} = E_{\text{pot}} + E_{\text{kin}}$$

The production tree of E is represented as:

### Usual programming

The calculation of E could be done in Fortran using subroutine calls to imperatively ask the program to realize the needed calculations, such as

    program compute_Energy
double precision :: E_nucl, E_pot, E_kin, E_elec, E

call compute_E_nucl(E_nucl)
call compute_E_pot(E_pot)
call compute_E_kin(E_kin)
call compute_E_elec(E_elec,E_pot,E_kin)
call compute_E(E,E_nucl,E_elec)

print *, 'Energy = ', E

end


In this example, it is not clear which are input and output arguments in the subroutine calls. A clearer way to express the same code would be using functions:

program compute_Energy
double precision :: E_nucl, E_pot, E_kin, E_elec, E
double precision :: compute_E_nucl, compute_E_pot, compute_E_kin, &
compute_E_elec, compute_E

E_nucl = compute_E_nucl()
E_pot  = compute_E_pot()
E_kin  = compute_E_kin()
E_elec = compute_E_elec(E_pot,E_kin)
E      = compute_E(E_nucl,E_elec)

print *, 'Energy = ', E

end


In both example, the programmer needs to know the production tree of E, in order to be position the statements in the correct order. For instance, the line

E_nucl = compute_E_nucl()


has to be positioned before

E      = compute_E(E_nucl,E_elec)


otherwise the program is wrong.

If the code is written in this way:

program compute_Energy
double precision :: compute_E_nucl, compute_E_pot, compute_E_kin, &
compute_E_elec, compute_E
print *, 'Energy = ', compute_E (compute_E_nucl(),  &
compute_E_elec (compute_E_pot(), compute_E_kin()) )

end


the production tree is expressed in the list of arguments, and the programmer does not need to worry about the sequence of the function calls. The call sequence is now handled by the compiler. Some compilers will call compute_E_nucl first, some others will call compute_E_elec first. However, for a real code, this practice is impossible because the code would be unreadable by a programmer.

### IRPF90 programming

If the parameters of function calls could be automatically inserted by a tool, the program would be as simple as

program compute_E
print *, 'Energy = ', E
end


The role of the IRPF90 tool is to allow programmers to write code with this style. IRPF90 is a program which generates Fortran90 code, from a language which is an extension of Fortran. In IRPF90, the concept of ‘‘entity of interest’’ or ‘‘IRP entity’’ is introduced. An IRP entity is a node of the production tree. It is defined by a provider function, whose role is to build the value of the entity. In this example, the provider function of E would be

BEGIN_PROVIDER [ double precision, E ]
E = E_nucl + E_elec
END_PROVIDER


where E_nucl and E_elec are also IRP entities. When an entity is used, if the entity has already been computed, the value of the last evaluation is returned. Otherwise, the code in the provider function is executed, and the result is returned. However, an entity can be invalidated (by modifying the value of a needed entity, for example), it will be recomputed. This mechanism guarantees that the same quantity is never computed more than once, and that when it is used it is always valid.

The main benefit of using IRPF90 is that the programmer never worries about the calling sequence of the code. As soon as he uses an entity, it is guaranteed that this entity is computed and valid. At first sight, with simple examples it is difficult to realize to what extent IRP programming makes things simpler. For a real code with thousands (millions) of lines, the code written with IRPF90 is as easy to read and modify as a code with a few hundreds of lines. Most of the complexity of a large code is now handled by the computer, and not the programmer.

## A simple example

Create a new directory named cube for example. Go into this directory and run the command

$irpf90 --init  Two temporary directories are created: $ ls
IRPF90_man  IRPF90_temp  Makefile


and a standard Makefile is build, using the gfortran compiler:

IRPF90 = irpf90  #-a -d
FC     = gfortran
FCFLAGS= -ffree-line-length-none -O2

SRC=
OBJ=
LIB=

include irpf90.make

irpf90.make: $(wildcard *.irp.f)$(IRPF90)


We can now start to write the code.

### The main program

First, we write a very simple program which prints the surface and the volume of a cube. In a file named cube_example.irp.f, write:

program cube_example
implicit none

print *, 'Surface Area :', surface
print *, 'Volume       :', volume
end



Remark that there is no explicit directive to run a computation. Hence, this code is clear as it expresses the intention of the programmer with a very epurated style : the goal of the main program is to print the surface and the volume. The way these quantities are computed should not appear here.

### The properties of the cube

The IRPF90 environment guarantees that when an entity is used, it is valid. In the main program, the action to print the variable surface will automatically request the value of the surface before the print statement : the value of the entity surface will be provided.

We can now write in the file named properties.irp.f how the properties are computed. The calculation of a property appears in the provider function of the property.

BEGIN_PROVIDER [ real, surface ]

BEGIN_DOC
! Surface of the cube
END_DOC

surface = 6. * edge**2
END_PROVIDER

BEGIN_PROVIDER [ real, volume ]

BEGIN_DOC
! Volume of the cube
END_DOC

volume = edge**3
END_PROVIDER


These two properties depend on the value of the edge variable which can be given in the standard input. The edge is the way we define a cube, so we write in a file named cube.irp.f:

BEGIN_PROVIDER [ real, edge ]
BEGIN_DOC
! Value of the edge of the cube
END_DOC

print *, "Value of the edge of the cube"
ASSERT (edge > 0.)
END_PROVIDER


Here the ASSERT keyword guarantees that when edge is provided, its value is positive. Otherwise, if the -a option of the irpf90 command is used, the program will fail will an error message:

 Stack trace:            0
-------------------------
cube_example
provide_center
provide_vertex
provide_edge
bld_edge
-------------------------
bld_edge: Assert failed:
file: cube.irp.f, line: 24
(edge > 0.)

edge  =   -1.000000


The assertion ensures that the value of edge will always be positive everywhere in the code.

The BEGIN_DOC ... END_DOC groups contain the documentation of the IRP entities, which helps to write dynamically the technical documentation of the program. The documentation of the IRP entities can be viewed through man pages using the irpman tool (shown in next section).

### Code compilation

To understand what happens at the execution, turn on the -a and -d options of irpf90 in the Makefile by removing the # in the first line. Then, run make.

$make Makefile:9: irpf90.make: No such file or directory irpf90 -a -d IRPF90_temp/cube.irp.F90 IRPF90_temp/properties.irp.F90 IRPF90_temp/cube_example.irp.F90 gfortran -ffree-line-length-none -O2 -c IRPF90_temp/cube.irp.F90 -o IRPF90_temp/cube.irp.o gfortran -ffree-line-length-none -O2 -c IRPF90_temp/properties.irp.F90 -o IRPF90_temp/properties.irp.o gfortran -ffree-line-length-none -O2 -c IRPF90_temp/cube_example.irp.F90 -o IRPF90_temp/cube_example.irp.o gfortran -ffree-line-length-none -O2 -c IRPF90_temp/irp_stack.irp.F90 -o IRPF90_temp/irp_stack.irp.o gfortran -ffree-line-length-none -O2 -c IRPF90_temp/irp_touches.irp.F90 -o IRPF90_temp/irp_touches.irp.o gfortran -o cube_example IRPF90_temp/cube_example.irp.o IRPF90_temp/irp_stack.irp.o IRPF90_temp/cube.irp.o IRPF90_temp/properties.irp.o IRPF90_temp/irp_touches.irp.o  Many files have been created: $ ls
cube_example        cube.irp.f       irpf90.make  IRPF90_temp  properties.irp.f
cube_example.irp.f  irpf90_entities  IRPF90_man   Makefile


For each *.irp.f file, a corresponding Fortran90 module has been built. The file irpf90.make was generated, and contains the dependencies between the *.irp.f files. The file irpf90_entities contains the list of the IRP entities, their type and the file in which they are defined:

$cat irpf90_entities cube.irp.f : real :: edge properties.irp.f : real :: surface properties.irp.f : real :: volume  Now, if you run: $ irpman surface


you obtain a man page describing the entity surface and its dependencies:

IRPF90 entities(l)                  surface                 IRPF90 entities(l)

Declaration
real :: surface

Description
Surface of the cube

File
properties.irp.f

Needs
edge

IRPF90 entities                     surface                 IRPF90 entities(l)


## Code execution

Recall that the -d and -a options were activated in the Makefile. Run the program, and choose 2 for the value of the edge of the cube:

$./cube_example 0 : -> provide_volume 0 : -> provide_edge 0 : -> edge Value of the edge of the cube 2. 0 : <- edge 0.0000000000000000 0 : <- provide_edge 0.0000000000000000 0 : -> volume 0 : <- volume 0.0000000000000000 0 : <- provide_volume 0.0000000000000000 0 : -> provide_surface 0 : -> surface 0 : <- surface 0.0000000000000000 0 : <- provide_surface 0.0000000000000000 0 : -> cube_example Surface Area : 24.000000 Volume : 8.0000000 0 : <- cube_example 0.0000000000000000  The debug option -d prints a lot of output. It corresponds to the exploration of the production trees of surface and volume, which are needed in the cube_example program. A right arrow tells us that we enter inside a subroutine, and the left arrow tells us that we leave the subroutine. When we leave a subroutine, the CPU time spent in the subroutine is printed (here, it is always 0 seconds). In this example, we can see that the print statements of the main program appear at the bottom of the output. Many things happen before the code we wrote. We first need to provide surface  -> provide_surface  As surface is not valid, we have to build it, but as surface needs edge, we first need to provide edge before computing the value of surface.  -> provide_edge  As edge is not valid, it has to be built.  -> bld_edge  Building edge asks the user to enter the value with the standard input.  Value of the edge of the cube  Now edge is valid  <- bld_edge 0.00000000000000 <- provide_edge 0.00000000000000  and we can build the value of surface:  -> bld_surface <- bld_surface 0.00000000000000  We are now back into the main program with a valid value for the surface. The value of volume is also requested in the main program, so the exploration of the production tree of volume starts:  -> provide_volume  volume needs edge. As edge is valid, it is not re-built at its value is used to calculate volume  -> bld_volume <- bld_volume 0.00000000000000 <- provide_volume 0.00000000000000  We can now execute the main program with valid values of surface and volume. -> cube_example  These values can now be used to be printed:  Surface Area : 24.00000 Volume : 8.000000  The last line tells us we leave the program <- cube_example 0.00000000000000  From this simple example, we can notice that a lot of energy has been saved for the programmer. First, the makefiles have been automatically generated. Then, the sequence of execution of the code is absolutely not controlled by the programmer. The only thing he had to worry about was the correctness of the definition of the entities of interest. Using IRPF90, there are questions that programmers will never ask anymore, for example: At this particular place of the code I need x. Is it already calculated? The programmer will just use x without worrying if it has been calculated or not, and he will be sure that its value is valid if the ASSERT statements have been properly inserted. ## Improvement of the example Every day, developers are improving already existing codes, which may or may not be written by them. Let’s try to add a new functionality to the code of the previous section: we now want to print the Cartesian coordinates of the center of the faces of a cube. To add this new feature, we have to introduce the coordinates of the vertices of the cube, find the groups of 4 vertices which constitute the faces, and calculate the centers. ### The main program In the main code, just add the information that you want to print the coordinates of the centers of the faces of the cube: program cube_example implicit none print *, 'Surface Area :', surface print *, 'Volume :', volume print *, '' print *, 'Centers of the faces:' integer :: i do i=1,face_num integer :: j print *, (center(j,i), j=1,3) end do end  In this code, the declarations of the integers ‘‘i’’ and ‘‘j’’ have been introduced just before their first use. In IRPF90, the declarations can appear anywhere. ### The addition of a new property Now, we introduce the ‘‘center’’ entity, which contains the values of the centers of the faces of the cube, in the properties.irp.f file: BEGIN_PROVIDER [ real, center, (3,face_num) ] implicit none BEGIN_DOC ! Coordinates of the center of the faces cube END_DOC integer :: i do i=1,face_num integer :: k do k=1,3 center(k,i) = 0. integer :: j do j=1,4 integer :: l l = face(j,i) center(k,i) = center(k,i) + vertex(k,l) enddo center(k,i) = center(k,i) / 4. enddo enddo END_PROVIDER  The center entity is an array of dimension (3,face_num), where face_num is the number of faces in a cube. For each center, the coordinates are computed as the average of the coordinates of the 4 vertices constituting the face. The coordinates of the vertices of the cube are present in the array vertex. The array face contains, for each face, the indices of the array vertex corresponding to the vertices of the face: these last arrays are defined in the cube.irp.f: BEGIN_PROVIDER [ integer, vertex_num ] implicit none BEGIN_DOC ! Number of vertices END_DOC vertex_num = 8 END_PROVIDER BEGIN_PROVIDER [ real, vertex, (3,vertex_num) ] implicit none BEGIN_DOC ! Coordinates of the vertices of the cube END_DOC integer :: k, i ! Initialize the array do i=1,vertex_num do k=1,3 vertex(k,i) = 0. enddo enddo ! The 1st point is the origin ! Build the 3 points on the axes do k=1,3 vertex(k,k+1) = edge enddo ! Build the 3 points in the xy, yz and zx planes integer :: knew(3) = (/2, 3, 1 /) do k=1,3 vertex(k,k+4) = edge vertex(knew(k),k+4) = edge enddo ! The last point do k=1,3 vertex(k,8) = edge enddo END_PROVIDER  For simplicity, the cube is chosen to have one point at the origin, and faces in the xy, yz and xz planes. The faces are computed using the squared distance matrix of the vertices: BEGIN_PROVIDER [ integer, face_num ] implicit none BEGIN_DOC ! Number of face of a cube END_DOC face_num = 6 END_PROVIDER BEGIN_PROVIDER [ integer, face, (4,face_num) ] implicit none BEGIN_DOC ! Indices of the vertices for each face of the cube END_DOC integer :: i, ii i=1 do ii = 0,1 ! Pick the 1st point and find the 3 points at 'edge' distance of it integer :: j, ifound(3), inext inext = 1 do j=1,vertex_num if (distance2(j,i) == edge2) then ifound ( inext ) = j inext = inext + 1 endif enddo ASSERT ( inext == 4 ) integer :: istart istart = 3*ii integer :: k, knew(3) knew(:) = (/ 2, 3, 1 /) do k=1,3 face(1,k+istart) = i face(2,k+istart) = ifound(k) face(3,knew(k)+istart) = ifound(k) enddo ! Find the 4th point of those 3 faces do j=1,vertex_num if (distance2(j,i) == 2.*edge2) then do k=1, 3 if ( (distance2(j,face(2,k+istart)) == edge2) .and. & (distance2(j,face(3,k+istart)) == edge2) ) then face(4,k+istart) = j endif enddo endif enddo ! Find the point opposite to the point i for 2nd iteration integer :: inew do j=1,vertex_num if (distance2(j,i) == 3.*edge2) then inew = j endif enddo i = inew end do END_PROVIDER  where the squared distance matrix is defined with: BEGIN_PROVIDER [ real, distance2, (vertex_num,vertex_num) ] implicit none BEGIN_DOC ! Squared distance matrix of the vertices END_DOC integer :: i, j, k do i=1,vertex_num do j=1,vertex_num distance2(j,i) = 0. do k=1,3 distance2(j,i) = distance2(j,i) + & (vertex(k,i) - vertex(k,j))**2 enddo enddo enddo END_PROVIDER  and the squared value of the edge is computed only once using: BEGIN_PROVIDER [ real, edge2 ] BEGIN_DOC ! edge2 : Square of the value of the edge END_DOC edge2 = edge**2 END_PROVIDER  ### Code execution Compile the program $ make
irpf90  -a -d
IRPF90_temp/cube.irp.F90
IRPF90_temp/properties.irp.F90
IRPF90_temp/cube_example.irp.F90
gfortran -ffree-line-length-none -O2 -c IRPF90_temp/cube.irp.F90 -o IRPF90_temp/cube.irp.o
gfortran -ffree-line-length-none -O2 -c IRPF90_temp/properties.irp.F90 -o IRPF90_temp/properties.irp.o
gfortran -ffree-line-length-none -O2 -c IRPF90_temp/cube_example.irp.F90 -o IRPF90_temp/cube_example.irp.o
gfortran -ffree-line-length-none -O2 -c IRPF90_temp/irp_touches.irp.F90 -o IRPF90_temp/irp_touches.irp.o
gfortran -o cube_example IRPF90_temp/cube_example.irp.o  IRPF90_temp/irp_stack.irp.o  IRPF90_temp/cube.irp.o
IRPF90_temp/properties.irp.o IRPF90_temp/irp_touches.irp.o


and run it:

$./cube_example 0 : -> provide_volume 0 : -> provide_edge 0 : -> edge Value of the edge of the cube 2 0 : <- edge 1.00000000000000002E-003 0 : <- provide_edge 1.00000000000000002E-003 0 : -> volume 0 : <- volume 0.0000000000000000 0 : <- provide_volume 1.00000000000000002E-003 0 : -> provide_center 0 : -> provide_vertex 0 : -> provide_vertex_num 0 : -> vertex_num 0 : <- vertex_num 0.0000000000000000 0 : <- provide_vertex_num 0.0000000000000000 0 : -> vertex 0 : <- vertex 0.0000000000000000 0 : <- provide_vertex 1.00000000000000002E-003 0 : -> provide_face_num 0 : -> face_num 0 : <- face_num 0.0000000000000000 0 : <- provide_face_num 0.0000000000000000 0 : -> provide_face 0 : -> provide_distance2 0 : -> distance2 0 : <- distance2 0.0000000000000000 0 : <- provide_distance2 0.0000000000000000 0 : -> provide_edge2 0 : -> edge2 0 : <- edge2 0.0000000000000000 0 : <- provide_edge2 0.0000000000000000 0 : -> face 0 : <- face 0.0000000000000000 0 : <- provide_face 0.0000000000000000 0 : -> center 0 : <- center 0.0000000000000000 0 : <- provide_center 1.00000000000000002E-003 0 : -> provide_surface 0 : -> surface 0 : <- surface 0.0000000000000000 0 : <- provide_surface 0.0000000000000000 0 : -> cube_example Surface Area : 24.000000 Volume : 8.0000000 Centers of the faces: 1.0000000 0.0000000 1.0000000 1.0000000 1.0000000 0.0000000 0.0000000 1.0000000 1.0000000 2.0000000 1.0000000 1.0000000 1.0000000 2.0000000 1.0000000 1.0000000 1.0000000 2.0000000 0 : <- cube_example 0.0000000000000000  ## Modification of the core of the program ### Modification of the input data In this section, we propose to modify the design of the cube. We want the user to give in input the Cartesian coordinates of the vertices, and the entity edge will be computed. We will show that this modification has minor impact on the rest of the code. In the cube.irp.f file, we first modify the provider of the edge entity. Considering that the vertices constitute a cube, the edge is the minimum value of the distance matrix BEGIN_PROVIDER [ real, edge ] BEGIN_DOC ! Value of the edge of the cube END_DOC edge = sqrt(edge2) END_PROVIDER BEGIN_PROVIDER [ real, edge2 ] BEGIN_DOC ! edge2 : Square of the value of the edge END_DOC integer :: i edge2 = huge(1.) do i=1,vertex_num do j=i+1,vertex_num edge2 = min(edge2,distance2(j,i)) enddo enddo END_PROVIDER  Then, we modify the provider of the vertex entity to read 8 points from the input file. BEGIN_PROVIDER [ real, vertex, (3,vertex_num) ] implicit none BEGIN_DOC ! Coordinates of the vertices of the cube END_DOC integer :: k, i ! Initialize the array print *, 'Vertices of the cube:' do i=1,vertex_num read(*,*) (vertex(k,i), k=1,3) enddo logical :: is_a_cube ASSERT ( is_a_cube(vertex) ) END_PROVIDER  To be sure that the data read by the code is valid, we write the function is_a_cube which returns .True. when the points given are vertices of a cube. This function is a standard Fortran function: logical function is_a_cube(v) implicit none real, intent(in) :: v(3,vertex_num) is_a_cube = .True. integer :: j do j=1,vertex_num-1 ! Choose a vector, then compute the dot product with all other vectors real :: dot(vertex_num) integer :: i do i=1,vertex_num dot(i) = 0. integer :: k do k=1,3 dot(i) = dot(i) + (v(k,i) - v(k,j))*(v(k,j+1) - v(k,j)) enddo enddo ! Sort the dot array integer :: pos(1) real :: temp do i=1,vertex_num pos = minloc(dot(i:)) pos(1) = pos(1) + i - 1 temp = dot(i) dot(i) = dot(pos(1)) dot(pos(1)) = temp enddo ! Normalize to unity real :: norm norm = dot(vertex_num) do i=1,vertex_num dot(i) = dot(i) / norm enddo ! Check the values of the dot products real :: ref(vertex_num) ref = (/ 0., 0., 0., 0., 1., 1., 1., 1. /) do i=1,vertex_num is_a_cube = is_a_cube .and. (dot(i) == ref(i)) enddo if (.not.is_a_cube) then is_a_cube = .True. ref = (/ 0., 0., 1., 1., 1., 1., 2., 2. /) ref = ref/2. do i=1,vertex_num is_a_cube = is_a_cube .and. (dot(i) == ref(i)) enddo endif if (.not.is_a_cube) then is_a_cube = .True. ref = (/ 0., 1., 1., 1., 2., 2., 2., 3. /) ref = ref/3. do i=1,vertex_num is_a_cube = is_a_cube .and. (dot(i) == ref(i)) enddo endif if (.not.is_a_cube) then return endif enddo end function  ### Code execution Build the new executable, and run the program : $ make
irpf90  -a -d
IRPF90_temp/cube.irp.F90
gfortran -ffree-line-length-none -O0 -g -c IRPF90_temp/cube.irp.F90 -o IRPF90_temp/cube.irp.o
gfortran -ffree-line-length-none -O0 -g -c IRPF90_temp/properties.irp.F90 -o IRPF90_temp/properties.irp.o
gfortran -ffree-line-length-none -O0 -g -c IRPF90_temp/debug.irp.F90 -o IRPF90_temp/debug.irp.o
gfortran -ffree-line-length-none -O0 -g -c IRPF90_temp/cube_example.irp.F90 -o IRPF90_temp/cube_example.irp.o
gfortran -o debug IRPF90_temp/debug.irp.o  IRPF90_temp/irp_stack.irp.o  IRPF90_temp/properties.irp.o  IRPF90_temp/cube.irp.o
gfortran -o cube_example IRPF90_temp/cube_example.irp.o  IRPF90_temp/irp_stack.irp.o  IRPF90_temp/properties.irp.o  IRPF90_temp/cube.irp.o

$./cube_example 0 : -> provide_volume 0 : -> provide_edge 0 : -> provide_edge2 0 : -> provide_distance2 0 : -> provide_vertex_num 0 : -> vertex_num 0 : <- vertex_num 0.0000000000000000 0 : <- provide_vertex_num 0.0000000000000000 0 : -> provide_vertex 0 : -> vertex Vertices of the cube: 0 0 0 2 2 2 2 0 0 2 2 0 0 2 0 0 0 2 0 2 2 2 0 2 0 : -> is_a_cube 0 : <- is_a_cube 0.0000000000000000 0 : <- vertex 0.0000000000000000 0 : <- provide_vertex 0.0000000000000000 0 : -> distance2 0 : <- distance2 0.0000000000000000 0 : <- provide_distance2 0.0000000000000000 0 : -> edge2 0 : <- edge2 0.0000000000000000 0 : <- provide_edge2 0.0000000000000000 0 : -> edge 0 : <- edge 0.0000000000000000 0 : <- provide_edge 0.0000000000000000 0 : -> volume 0 : <- volume 0.0000000000000000 0 : <- provide_volume 0.0000000000000000 0 : -> provide_center 0 : -> provide_face_num 0 : -> face_num 0 : <- face_num 0.0000000000000000 0 : <- provide_face_num 0.0000000000000000 0 : -> provide_face 0 : -> face 0 : <- face 0.0000000000000000 0 : <- provide_face 0.0000000000000000 0 : -> center 0 : <- center 0.0000000000000000 0 : <- provide_center 0.0000000000000000 0 : -> provide_surface 0 : -> surface 0 : <- surface 0.0000000000000000 0 : <- provide_surface 0.0000000000000000 0 : -> cube_example Surface Area : 24.000000 Volume : 8.0000000 Centers of the faces: 1.0000000 0.0000000 1.0000000 1.0000000 1.0000000 0.0000000 0.0000000 1.0000000 1.0000000 2.0000000 1.0000000 1.0000000 1.0000000 2.0000000 1.0000000 1.0000000 1.0000000 2.0000000 0 : <- cube_example 0.0000000000000000  The result is the same as what was obtained in the previous section, but now we can see that the sequence of the code is different. The entities of interest are computed in a different order. ## Changing value of entities In real applications, iterative processes are often used, and the values of entities change. In this section, we show how modification of entities is realized. ### The iterative program We write a new program which prints the value of the surface of the cube, as long as the value of the surface is below a threshold. At the end of one iteration, the length of the edge is incremented by the value increment. In file iterative_test.irp.f, write: program iterative_test implicit none do while (surface < threshold) print *, surface edge = edge + increment TOUCH edge enddo end program  In this iterative process, the IRP entity edge is modified. The TOUCH keyword is mandatory informs the IRPF90 that the value of edge is valid, but all the values of the entities which depend on edge are not valid anymore, and have to be provided again. The threshold and increment values are given in input, in file control.irp.f: BEGIN_PROVIDER [ real, threshold ] BEGIN_DOC ! Threshold for the value of the surface END_DOC print *, 'Threshold for the surface:' read (*,*) threshold ASSERT (threshold >= 0.) END_PROVIDER BEGIN_PROVIDER [ real, increment ] BEGIN_DOC ! The increment of the value of the edge at each iteration END_DOC print *, 'Increment of the edge' read(*,*) increment ASSERT (increment > 0.) END_PROVIDER  Now, if you build the program $ make
irpf90  -a -d
gfortran -ffree-line-length-none -O0 -g -c IRPF90_temp/control.irp.F90 -o IRPF90_temp/control.irp.o
gfortran -o cube_example IRPF90_temp/cube_example.irp.o  IRPF90_temp/irp_stack.irp.o
IRPF90_temp/properties.irp.o  IRPF90_temp/control.irp.o  IRPF90_temp/cube.irp.o
gfortran -o debug IRPF90_temp/debug.irp.o  IRPF90_temp/irp_stack.irp.o  IRPF90_temp/properties.irp.o
IRPF90_temp/control.irp.o  IRPF90_temp/cube.irp.o
gfortran -ffree-line-length-none -O0 -g -c IRPF90_temp/iterative_test.irp.F90 -o IRPF90_temp/iterative_test.irp.o
gfortran -o iterative_test IRPF90_temp/iterative_test.irp.o  IRPF90_temp/irp_stack.irp.o
IRPF90_temp/properties.irp.o  IRPF90_temp/control.irp.o  IRPF90_temp/cube.irp.o


you can remark that the executable cube_example of the previous section is still built, and a new executable iterative_test is created.

Running the program gives:

$./iterative_test 0 : -> provide_threshold 0 : -> threshold Threshold for the surface: 100. 0 : <- threshold 0.00000000000000 0 : <- provide_threshold 0.00000000000000 0 : -> provide_edge 0 : -> provide_edge2 0 : -> provide_distance2 0 : -> provide_vertex_num 0 : -> vertex_num 0 : <- vertex_num 0.00000000000000 0 : <- provide_vertex_num 0.00000000000000 0 : -> provide_vertex 0 : -> vertex Vertices of the cube: 0 0 0 2 2 2 2 0 0 2 2 0 0 2 0 0 0 2 0 2 2 2 0 2 0 : -> is_a_cube 0 : <- is_a_cube 0.00000000000000 0 : <- vertex 0.00000000000000 0 : <- provide_vertex 0.00000000000000 0 : -> distance2 0 : <- distance2 0.00000000000000 0 : <- provide_distance2 0.00000000000000 0 : -> edge2 0 : <- edge2 0.00000000000000 0 : <- provide_edge2 0.00000000000000 0 : -> edge 0 : <- edge 0.00000000000000 0 : <- provide_edge 0.00000000000000 0 : -> provide_increment 0 : -> increment Increment of the edge 1. 0 : <- increment 0.00000000000000 0 : <- provide_increment 0.00000000000000 0 : -> provide_surface 0 : -> surface 0 : <- surface 0.00000000000000 0 : <- provide_surface 0.00000000000000 0 : -> iterative_test 24.00000 0 : -> touch_edge 0 : <- touch_edge 0.00000000000000 0 : -> provide_surface 0 : -> surface 0 : <- surface 0.00000000000000 0 : <- provide_surface 0.00000000000000 54.00000 0 : -> touch_edge 0 : <- touch_edge 0.00000000000000 0 : -> provide_surface 0 : -> surface 0 : <- surface 0.00000000000000 0 : <- provide_surface 0.00000000000000 96.00000 0 : -> touch_edge 0 : <- touch_edge 0.00000000000000 0 : -> provide_surface 0 : -> surface 0 : <- surface 0.00000000000000 0 : <- provide_surface 0.00000000000000 0 : <- iterative_test 0.00000000000000  In this example, it appears clearly that when the edge value is modified, only the surface is computed again. The volume is invalid, but as it is not requested, it is not computed. ## Embedding shell scripts It is common practice to use shell scripts to gather data at compilation time. In the IRPF90 environment, shell scripts can be directly introduced in the code. Let us write a simple header for the code, which returns the name of the user who compiled the code, and the date of compilation. We now remove the -d option of irpf90 for shorter outputs. program iterative_test implicit none print *, 'Program ', irp_here BEGIN_SHELL [ /bin/sh ] echo "print *, \'Compiled by :$USER \'"
echo "print *, \'Compilation date: date\'"
END_SHELL

do while (surface < threshold)
print *, surface
edge = edge + increment
TOUCH edge
enddo
end program


Running this program returns the following output:

 Threshold for the surface:
100
Vertices of the cube:
0 0 0
2 2 2
2 0 0
2 2 0
0 2 0
0 0 2
0 2 2
2 0 2
Increment of the edge
1
Program iterative_test
Compiled by : scemama
Compilation date: Fri Sep 25 16:02:22 CEST 2009
24.00000
54.00000
96.00000


First, note the use of the irp_here variable. This is a character*(*) variable which takes as value the name of the subroutine or function in which it is used. Then, you can remark that the print statements were executed after gathering information from the input. This is due to the fact that in IRPF90, the entities are provided as soon as possible. If you really want to print the header at the beginning of the program, you can use the following trick:

program iterative_test
implicit none

print *, 'Program ', irp_here
BEGIN_SHELL [ /bin/sh ]
echo "print *, \'Compiled by : $USER \'" echo "print *, \'Compilation date: date\'" END_SHELL call run_iterative_process end program subroutine run_iterative_process implicit none do while (surface < threshold) print *, surface edge = edge + increment TOUCH edge enddo end program  which gives the output:  Program iterative_test Compiled by : scemama Compilation date: Fri Sep 25 16:03:58 CEST 2009 Threshold for the surface: 100 Vertices of the cube: 0 0 0 2 2 2 2 0 0 2 2 0 0 2 0 0 0 2 0 2 2 2 0 2 Increment of the edge 1 24.00000 54.00000 96.00000  Shell scripts can also be used to write templates. For example, if you need to sort arrays of real, double precision or integers, you can use the following Python script: BEGIN_SHELL [ /usr/bin/python ] for i in [('' ,'real'), \ ('d','double precision'), \ ('i','integer'), \ ]: print "subroutine "+i[0]+"sort (x,iorder,isize)" print " implicit none" print " "+i[1]+" :: x(*), xtmp" print " integer :: iorder(*)" print " integer :: isize" print " integer :: i, i0, j, jmax" print "" print " do i=1,isize" print " xtmp = x(i)" print " i0 = iorder(i)" print " do j=i-1,1,-1" print " if ( x(j) > xtmp ) then " print " x(j+1) = x(j)" print " iorder(j+1) = iorder(j)" print " else" print " exit" print " endif" print " enddo" print " x(j+1) = xtmp" print " iorder(j+1) = i0" print " enddo" print "" print "end" print ""  which builds in one shot three subroutines: • isort for integers • dsort for double precision • sort for reals Entities of interest can also be generated by scripts. The following example (documentation.irp.f) builds a character*(*) IRP entity for each entity which contains its documentation: BEGIN_SHELL [ /usr/bin/python ] import os doc = {} for filename in os.listdir('.'): if filename.endswith('.irp.f'): file = open(filename,'r') inside_doc = False for line in file: if line.strip().lower().startswith('begin_provider'): name = line.split(',')[1].split(']')[0].strip() doc[name] = "" elif line.strip().lower().startswith('begin_doc'): inside_doc = True elif line.strip().lower().startswith('end_doc'): inside_doc = False elif inside_doc: doc[name] += line[1:].strip()+" " file.close() lenmax = 0 for e in doc.keys(): lenmax = max(len(e),lenmax) print "BEGIN_PROVIDER [ character*(%d), entities, (%d) ]"%(lenmax,len(doc)) print " BEGIN_DOC" print "! List of IRP entities" print " END_DOC" for i,e in enumerate(doc.keys()): print "entities(%d) = '%s'"%(i+1, e) print "END_PROVIDER" for e in doc.keys(): print "BEGIN_PROVIDER [ character*(%d), %s_doc ]"%(len(doc[e]),e) print " BEGIN_DOC" print "! Documentation of variable %s"%(e,) print " END_DOC" print " %s_doc = '%s'"%(e,doc[e]) print "END_PROVIDER" END_SHELL  and a new main program is created (get_doc.irp.f) to print the documentation of a variable if it is present in the command line: program get_doc integer :: iargc character*(32) :: arg integer :: i, j if (iargc() == 0) then print *, 'List of IRP entities' do j=1,size(entities) print *, entities(j) enddo return endif do i=1,iargc() call getarg(i,arg) BEGIN_SHELL [ /usr/bin/python ] import os entities = [] for filename in os.listdir('.'): if filename.endswith('.irp.f'): file = open(filename,'r') for line in file: if line.strip().lower().startswith('begin_provider'): name = line.split(',')[1].split(']')[0].strip() entities.append(name) file.close() for e in entities: print " if (arg == '%s') then"%(e,) print " print *, %s_doc"%(e,) print " endif" END_SHELL enddo end  Execution of this code gives: $ ./get_doc
List of IRP entities
distance2
center
vertex
surface
face
volume
vertex_num
edge2
edge
increment
threshold
face_num

\$ ./get_doc volume
Volume of the cube


## Other features

### Freeing memory

Memory of an IRP entity can be freed using the FREE keyword

 FREE x


where x is an array entity. The memory occupied by x will be freed, and its status will be tagged as invalid. If x is needed later, the memory will be re-allocated, and x will be re-built. If it is not an array, the FREE keyword will only mark it as invalid.

### Conditional compilation

Conditional compilation is possible using the IRP_IF ... IRP_ELSE .. IRP_ENDIF directives.

IRP_IF MPI
include 'mpif.h'
print *, 'Multiprocessor code'
IRP_ELSE
print *, 'Monoprocessor code'
IRP_ENDIF


Compiling the previous code with irpf90 -DMPI will compile code suitable for the use of the MPI library, otherwise, the mono-processor code will be compiled.

## Conclusion

Many observations can be made from this simple example.

In the first section, we started to write a simple code. At the time we wrote code, we did not build the design for future improvement: only the edge length of the cube was needed.

Then, we wanted to compute another property depending on the coordinates of the vertices. This quantity was easily introduced, without any interference with the code which was written before.

Then, we chose to change the internal representation of the cube. The user gave in input the coordinates of the vertices and the edge value was computed from them. Making this modification did not interfere at all with the rest of the program.

From this example, we can conclude that, using the IRPF90 environment, scientific programming is simpler. This simplicity of writing code lets the scientific programmer focus on science instead of focusing on memory allocation or makefiles.

The code is also clearer, since the information is very localized. There is only one way to compute a quantity, and it is located in the provider of this quantity.

The use of embedded scripts allows the programmer to reduce considerably the number of lines of code, and also to automatically update certain parts of the code upon modification. For instance, in the presented example, if the programmer adds a new IRP entity, the documentation program will be automatically updated.

The resulting code is usually faster than code written in Fortran. Indeed, as the programmer is forced to partition his code in small functions (providers), very few memory locations are used en each function and the compiler can memory accesses are well optimized. Moreover, programmers will write (unintentionally) code which will be easier for the compilers to optimize.