Comparison and Evaluation of Floating Point Representations in IBM/370 and VAX-11/80
Each computer system supports a set of data types which serve as standard interfaces between the user and the computer, and between the computer and peripheral devices. There are scientific applications where, from the user’s point of view, the numerical accuracy is an important quality factor. According to Knuth (1981), the concept of floating point representation can be traced back to Babylonian mathematicians (about 1800 B.C.); the machine use of floating point representation was independently proposed by Leonardo Torres y Quevedo (Madrid, 1914), Konrad Zuse (Berlin, 1936), and George Stibitz (New Jersey, 1939).
Floating point computation is inexact and, if not used properly, it is entirely possible to come up with answers that may consist almost entirely of “noise”. For scientific applications, it is important to understand the floating point architecture of the machine being used, and make necessary accommodations in the algorithms for problem solving. This impacts on the portability of data across machines.
The authors examined the data types supported by IBM/370 and VAX-11/780 for purposes of comparison and evaluation. The floating point representations in the two present some interesting comparisons that are summarized in the theories derived in the paper. We found the magnitude range of values on a 4-byte long storage area is better for IBM than for VAX. However, for a certain range of values, VAX has a better precision than IBM on a 4-byte long floating point representation. Similar results for double and quad word floating point numbers on the two machines have also been provided.
We use our analysis to identify steps to be taken towards building a methodology that offers a high degree of portability and interoperability of data across different hardware architectures.
KeywordsFloating Point Magnitude Range Float Point Number Float Point Representation Floating Point Data
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