No abstract

No abstract

In current higher level languages arrays are parallelepiped in N dimensions, each dimension having an index range from a lower limit to an upper limit (both must be integers), the increment between valid index values being one.By removing the r e s t r i ction of limits and increments to be integers or unity, a homogenously addressed sections or t e a s of an array is defined. Co~.~ining several of these regions each with its own limits and increments but with com~non addressin~forms an array with varying data density.These new arrays are referred to as Varying Density Arrays (VDA).All data elements of a given region are restricted to a single format and structure.The element structure and format of one region in no way restricts elements in other regions. This generalization permits uniform addressing of conventional arrays, VDAs and PL/I or COBOL structures. This paper discusses (i) the concept of a VDA, (2) extensions to PL/I declarations to allow the definition of VDAs, (3) gives examples in PL/I and APL and discusses operations of VDAS and their subarrays.The paper touches on, but does not discuss, mappings to physical storage.

Several authors have considered the problem of control of program flow in secondary (user-written) functions in APL and forms which would give APL equivalents of the control structures of more traditional languages have been proposed. Rather than expanding or altering the means of controlling program flow in APL, this paper suggests restricting the forms, but not the power, of branching.The motivation and implications are presented and the advantages and disadvantages are weighed.Problems of migration of functions and questions regarding the resumption of suspended functions are considered. Consideration of function call and the system variable, DLC, suggests a generalization of secondary-function execution with regard to program flow among userwritten functions.This provides an alternate view of suspended functions and permits branching to be generalized to include co-routines.

The task of evaluating the cumulative distribution of a normally distributed random variable is considered. A brief introduction into this problem is given and several possible approximations are presented as APL functions. Many of these functions have been written in two versions. The first version is written in the original APL style. the companion function using an APL2 coding style is also included in the paper for purposes of comparison. Both versions have been tested using simple data vectors of varying lengths and run under APL on an IBM 3090 with and without a Vector Facility. The results are compared among the algorithms, between the coding styles, and with and without hardware support for vector processing.