Automatic translation of FORTRAN programs to vector form

Abstract

The recent success of vector computers such as the Cray-1 and array processors such as those manufactured by Floating Point Systems has increased interest in making vector operations available to the FORTRAN programmer. The FORTRAN standards committee is currently considering a successor to FORTRAN 77, usually called FORTRAN 8x, that will permit the programmer to explicitly specify vector and array operations.Although FORTRAN 8x will make it convenient to specify explicit vector operations in new programs, it does little for existing code. In order to benefit from the power of vector hardware, existing programs will need to be rewritten in some language (presumably FORTRAN 8x) that permits the explicit specification of vector operations. One way to avoid a massive manual recoding effort is to provide a translator that discovers the parallelism implicit in a FORTRAN program and automatically rewrites that program in FORTRAN 8x.Such a translation from FORTRAN to FORTRAN 8x is not straightforward because FORTRAN DO loops are not always semantically equivalent to the corresponding FORTRAN 8x parallel operation. The semantic difference between these two constructs is precisely captured by the concept of dependence. A translation from FORTRAN to FORTRAN 8x preserves the semantics of the original program if it preserves the dependences in that program.The theoretical background is developed here for employing data dependence to convert FOR-TRAN programs to parallel form. Dependence is defined and characterized in terms of the conditions that give rise to it; accurate tests to determine dependence are presented; and transformations that use dependence to uncover additional parallelism are discussed.

Whole-function vectorization

“…A lot of research went into parallelizing scientific (Fortran) programs; especially the analysis and automatic transformation of loop nests [9], [10]. Allen et al [2] pioneered control flow to data flow conversion to help the dependence analyses to cope with more complex control structures.…”

A Dimension Abstraction Approach to Vectorization in Matlab

“…The same idea can be applied to the vectorization of Matlab code: if many loop iterations can be done independently, a vector of the operands can be supplied to a vector operation instead. The foundation for a vectorizing compiler [2] and techniques to increase the amount of vectorization [19] now appears in textbooks [1,22]. In particular, the dependencebased vectorizer of Allen & Kennedy served as the basis for our vectorizer.…”

Analysis and transformation in an interactive parallel programming tool

“…This kind of anomaly, often called a data race, precludes the parallelization of the above loop. In the literature of compilation for parallel execution, a potential data race is referred to as a loop-carried dependence 3,34]. Without explicit synchronization, only loops with no carried dependences may be safely executed in parallel.…”

“…A dependence is carried by the outermost loop for which the element in the direction vector is not aǹ ='. Additionally, direction vectors are used to determine the safety and pro tability of loop interchange 3,48]. Distance vectors are more precise versions of direction vectors that specify the actual number of loop iterations between two accesses to the same memory location 3,48].…”

“…Additionally, direction vectors are used to determine the safety and pro tability of loop interchange 3,48]. Distance vectors are more precise versions of direction vectors that specify the actual number of loop iterations between two accesses to the same memory location 3,48]. They are employed by transformations to exploit parallelism and the memory hierarchy.…”