Models of Data Structures in the Main Memory

Computerized data processing based on DL coding may be realized by the method of processing with a fixed number of significant digits in DL data [1-2]. This method of data processing relies on choosing the variation boundary of the number Q for all DL structures found during the solution of a given problem. The process of calculation and the involved DL data with a fixed number _fixed of significant units are presented schematically in Fig. 3.1, showing a field length of DL codes that can be reached only in theory. As follows from Fig. 3.1, the field length of DL codes in all data is not more than the fixed value _fixed

Fig.3.1. Illustration of a calculation process with a fixed value _fixed

In this algorithm of processing, the operands in each arithmetic operation are limited by the value _fixed. The result of each operation is tested whether the field length of DL codes exceeds _fixed. If there is no excess, the result remains unchanged, otherwise _fixed is assigned to . This limitation of DL numbers is performed only within a fixed range and is not defined by the mantissa length. The range, in its turn, is determined by the given maximal and minimal possible values of the digits of a DL number. Setting the parameter _fixed, you can define the volume of memory necessary for solving the task at the beginning of the processing.

When defining _fixed, the following should be taken into account:

- a very large _fixed, increases the accuracy of calculation, the volume of memory used, and the processing time;

- in the case of a small _fixed, all these parameters decrease.

A situation may occur when _fixed will be so small that the result of processing will be incorrect.

It follows from the mentioned above, that the problem of obtaining an acceptable accuracy of calculation using the method of processing based on DL arithmetic with a fixed _fixed has an ambiguous solution.

It is important to develop a model of calculation which would allow finding an optimal number of significant digits in DL structures for problem solving with a necessary accuracy.

Another variant of computerized data processing based on using DL structures is the method of processing with an adaptive value of the number Q of significant digits in DL data [1-2].

In this method of processing, there are no limitations on Q. In data processing that value of Q_ad is used this is equal to the maximal value of Q among all the DL structures at the beginning of solving a given problem. The given value does not limit the bit length of the result and is used as an initial in the method of accuracy-based adaptation.

The process of calculation and the involved DL data with an adaptive value Q_ad of the number of significant digits, are shown schematically in Fig. 3.2.

Fig.3.2. Illustration of a calculation process with an adapted value Q_ad.

Fig.3.2 shows that Q_ad may vary during data processing.

This method of processing, as well as previous variant, enhances the capabilities of a computer as far as the accuracy indices are concerned. Besides, both mantissa normalization procedure and results rounding procedure are eliminated here. The range of DL data is limited not by the method of processing, but only by the length of binary words which represent the values of DL code digits in the computer environment during data storage, transportation, and processing.

The length of the working field of DL data is adjusted, in an adaptive manner, to the precision of the computational problem being solved. If the number of bits in the result А of a certain computing operation exceeds Q_ad (the value of ) necessary for faithful result representation, the number of bits will not be limited. Q_ad, in its turn, will become equal to the newly increased value of .

The range of DL data is also adaptive by precision as the variation boundaries of the values and , both in an individual DL datum and in the whole computational problem, will be limited not only by the range limits but by the number of significant digits as well. The parameters and change freely depending on the operation performed and the values of operands. Therefore, the considered variant of using DL structures in computer processing allows adaptive variations of the data representation range, which satisfies the processing precision.

The adaptive method of processing is limited by the used memory and time recourse. The greater the value Q_ad becomes, the larger volume of memory is necessary to represent DL data, and more time will be used for processing. So, this variant of computer processing based on DL data representation also does not give an unambiguous solution of the problem of assuring an acceptable accuracy. A computational model should be developed that would save time and memory spent on data processing with the minimal loss in the accuracy of the results of DL operations.

Date: 2015-12-24; view: 753