FORTRAN scalar

Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (1992). Numerical Recipes in Fortran 77 The Art of Scientific Computing (2nd edn). Cambridge University Press. Rajagopalan, A. G. and C. Tong (2003). Experimental investigation of scalar-scalar-... 

With the advent of vector processors over the last ten years, the vector computer has become the most efficient and in some instances the only affordable way to solve certain computational problems. One such computer, the Texas Instruments Advanced Scientific Computer (ASC), has been used extensively at the Naval Research Laboratory to model atmospheric and combustion processes, dynamics of laser implosions, and other plasma physics problems. Furthermore, vectorization is achieved in these programs using standard Fortran. This paper will describe some of the hardware and software differences which distinguish the ASC from the more conventional scalar computer and review some of the fundamental principles behind vector program design. 

This integration method can be optimized for the ASC in two steps. The first is to construct the code so that vectorization over each set of equations occurs. Here the main problem is the decision process associated with the application of the "stiff" or "normal" formulas to each equation. If these formulas are implemented in the usual fashion with an IF test in the appropriate DO Loops the smooth flow of contiguous data from core through the CPU will be inhibited and scalar code will result. Optimization of this process can be accomplished by calculating both formulas and applying a multiplicative factor 0 or 1. The following example of Fortran code illustrates this technique. 

Almost all applications programming in chemistry, and structural chemistry in particular, is performed in the FORTRAN language and the molecular mechanics calculations for which this hardware/software design exercise was undertaken is no exception. There are two problems which must be solved in order to build a FORTRAN microcomputer system with good scalar and array computational performance and these are firstly, the design of an efficient scalar processor with a transparent FORTRAN interface to the hardware and secondly, the design of an efficient AFPP,... 

Scalar Fortran Coding of Gauss-Jordan Matrix Inverter... 

The are invariant under a rotation of the entire system, since they depend only on a length (the separation R) and on scalar products (the direction cosines), and are also unchanged by simultaneous exchange of the subscripts and superscripts = 7 ". All the to terms in R have been calculated [13], and are tabulated in Table 2. Notice that the orientations and of the two sites do not appear explicitly in these expressions, but only implicitly through the direction cosines etc. In fact it is never necessary to evaluate any trigonometric functions to obtain the T l. A computer program in FORTRAN 77 is available from the author to evaluate the and the electrostatic energy for a system of multipoles. 

One class of mainframe now available is the vector processor, which is optimised for operations on consecutive elements of arrays, which, in FORTRAN, often means DO loops. Might not these processors provide a speeding up of the DO loops The answer is no, because each DO loop only involves perhaps one addition to the abundances. But nevertheless the speed of these processors is often such that they are to be preferred to normal, scalar machines. 

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