Parsing a complicated function using MKL/VML - arrays

Question

I am trying to calculate a fairly complicated function, say func() - involving several additions, substractions, multiplications, divisions and trigonometric functions, of several two-dimensional arrays in fortran. The calculation is massively parrallel, in that each func() is independent over its row and column location. Each of the matrices is many gigabytes in size, and there are about a dozen of them as arguments.
I would like to make use of Intel MKL functions (invoking --mkl-parallel), in particular VML functions to add, subtract, divide etc. My question is: how can I render a complicated functional expression such as,
e.g.: func(x,y,z) = x*y+cos(z*x-x) where x,y,z are 2d arrays of several GB
in terms of VML functions but using more familiar binary operators. You see my problem requires, in principle, converting all the binary operators, such as "+" and "*" into binary functions taking arguments as ?vadd(x,y). Of course this would be very cumbersome and unsightly for large expressions. Is there a way to overload the binary arithmetic operators such as "+","-" to preferentially use MKL/VML versions in fortran. An example would be nice! Thanks!

Answer 1

I know this answer is a little bit off-topic.
Since all the operations are element-wise and your operations are simple, the func() could be a memory bandwidth bounded task. In this case, using VML may not be a good choice to maximum the performance.
Suppose each of your arrays is of 10GB in size, uisng VML as follows will need at least 9 x 10GB reading and 5 x 10GB writing.
func(...) {
tmp1=x*z
tmp1=tmp1-x;
tmp1=cos(tmp1);
tmp2=x*y;
return tmp1+tmp2;
}
where all the operations all overloaded for 2d array.
Instead you may find the following approach has much less memory access (3 x 10GB reading and 1 x 10GB writing) thus could be quicker (pseudo code).
$omp parallel for
for i in 1 to m
for j in 1 to n
result(i,j)= x(i,j)*y(i,j)+cos(z(i,j)*x(i,j)-x(i,j));
end
end

Answer 2

I developped a small example to show the addition of two vectors. As I don't have MKL installed anymore, I used the SAXPY command from BLAS. The principle should be the same.
At first you define a module with the appropriate definitions. In my case this would be an assignment to save a real array in my datatype (this is only a convenience function as you could also directly access the array variable) and the definition of the addition. Both are a new overload to the + operator and = assignment.
In the program, I define three fields. Two of them get assigned with random numbers and then added to get the third field. Then the first two fields get stored in my special variables, and the result of this addition is stored in a third variable of this type.
Finally, the result is compared by accessing the array directly. Please note, that the assignment from custom datatype to the same datatype is already defined (e.g. ffield3 = ffield1 is already defined.)
My module:
MODULE fasttype
IMPLICIT NONE
PRIVATE
PUBLIC :: OPERATOR(+), ASSIGNMENT(=)
TYPE,PUBLIC :: fastreal
REAL,DIMENSION(:),ALLOCATABLE :: array
END TYPE
INTERFACE OPERATOR(+)
MODULE PROCEDURE fast_add
END INTERFACE
INTERFACE ASSIGNMENT(=)
MODULE PROCEDURE fast_assign
END INTERFACE
CONTAINS
FUNCTION fast_add(fr1, fr2) RESULT(fr3)
TYPE(FASTREAL), INTENT(IN) :: fr1, fr2
TYPE(FASTREAL) :: fr3
INTEGER :: L
L = SIZE(fr2%array)
fr3 = fr2
CALL SAXPY(L, 1., fr1%array, 1, fr3%array, 1)
END FUNCTION
SUBROUTINE fast_assign(fr1, r2)
TYPE(FASTREAL), INTENT(OUT) :: fr1
REAL, DIMENSION(:), INTENT(IN) :: r2
INTEGER :: L
IF (.NOT. ALLOCATED(fr1%array)) THEN
L = SIZE(r2)
ALLOCATE(fr1%array(L))
END IF
fr1%array = r2
END SUBROUTINE
END MODULE
My program:
PROGRAM main
USE fasttype
IMPLICIT NONE
REAL, DIMENSION(:), ALLOCATABLE :: field1, field2, field3
TYPE(fastreal) :: ffield1, ffield2, ffield3
ALLOCATE(field1(10),field2(10),field3(10))
CALL RANDOM_NUMBER(field1)
CALL RANDOM_NUMBER(field2)
field3 = field1 + field2
ffield1 = field1
ffield2 = field2
ffield3 = ffield1 + ffield2
WRITE(*,*) field3 == ffield3%array
END PROGRAM