Современные средства аппаратной и программной поддержки IEEE-стандарта
Journal Title: Математичне моделювання - Year 2017, Vol 1, Issue 1
Abstract
MODERN MEANS OF HARDWARE AND SOFTWARE SUPPORT FOR THE IEEE STANDARD Zhulkovska I.I., Zhulkovskii O.A. Abstract Rounding floating-point numbers is a very important problem of the existing computer arithmetic. Numbers are rounded when you enter initial values and after each arithmetic operation. Uniform standard for binary representation of floating point numbers was developed and implemented by the Association IEEE (Institute of Electrical and Electronics Engineers). The IEEE 754 introduces the following required for realization rounded floating-point operations: addition, multiplication, subtraction, division, calculating the remainder of the division, square root, format conversion. Problem is improving the reliability of simulation results based on the evaluation of modern, most commonly used, hardware and software tools for obtaining the highest accuracy of computations and reducing errors due to the representation of actual data in computer memory. Improving the accuracy of arithmetic operations by increasing the bit numbers is the main means performing calculations critical to rounding. Modern general-purpose processors and high level language compilers maintain, as a rule, only formats single and double precision, as well as not defined standard double extended precision format in which the mantissa consists of 64 bits. Arithmetic increased accuracy is costly, and therefore implemented in software. The constant presence of rounding errors when working with the machine arithmetic imposes special requirements to computer algorithms and requires additional analysis of the problem being solved. Almost all numbers are represented in the computer memory with an error, so you need to know how the decision sensitive to changes in the parameters of the task. The study shows the capabilities of modern general-purpose processors and high-level language compilers to support high-precision formats and modern streaming processing technologies to improve the efficiency of mathematical modeling. References [1] IEEE Standard for Floating-Point Arithmetic, New York, 2008, 70p. [2] Hanrot G., Lefevre V., Muller J.-M., Revol N. and other. Some Notes for a Proposal for Elementary Function Implementation in Floating-Point Arithmetic, Proc. of Workshop IEEE 754 and Arithmetic Standardization, in ARITH-15, 2001. [3] Defour D., Hanrot G., Lefevre V., Muller J.-M. and other. Proposal for a standardization of mathematical function implementation in floating-point arithmetic. Numerical Algorithms, 2004, no.37(1–4), рр. 367–375. [4] Aharoni M., Asaf S., Fournier L., Koifman A. and other. A Test Generation Framework for Datapath Floating-Point Verification. IEEE International High Level Design Validation and Test Workshop, 2003, рр. 17–22. [5] Stehle D., Lefevre V., Zimmermann P. Searching Worst Cases of a One-Variable Function Using Lattice Reduction. IEEE Transactions on Computers, 2005, no.54(3), рр. 340–346. [6] Nikonov O.Ya, Mnushka O.V., Savchenko V.M. “Otsenka tochnosti vychisleniy spetsial'nykh funktsiy pri razrabotke kompyuternykh programm matematicheskogo modelirovaniya”. Visnyk NTU «KHPI» [Bulletin of the NTU "KhPI"],2011, no.17, рр. 115–121 (in Russian). [7] Zhulkovska I.I., Zhulkovskii O.O., Shaganenko R.G. Vychisleniye granichnykh znacheniy subnormalnykh chisel v IEEE-standarte. Matematychne modelyuvannya – Mathematical modeling, 2015, no.1 (32), рр. 41–44 (in Russian). [8] Zhulkovska I.I., Zhulkovskii O.O., Nikolayenko Yu.V. “Vychisleniye granichnykh znacheniy deystvitelnykh chislovykh dannykh v IEEE-standarte”. Zbirnyk naukovykh prats DDTU (tekhnichni nauky) [Collection of sciences works of DSTU (technical sciences)], 2015, no.1 (26), рр. 240–245 (in Russian). [9] Goldberg D. What Every Computer Scientist Should Know about Floating-Point Arithmetic. ACM Computing Surveys, 1991, no.23(1), рр. 5–48. [10] Zhulkovska I.I., Zhulkovskii O.O. Vychisleniye maksimalnykh absolyutnykh pogreshnostey okrugleniya chisel v IEEE-standarte. Matematychne modelyuvannya – Mathematical modeling, 2015, no.2 (33), рр. 33–36 (in Russian).
Authors and Affiliations
И. И. Жульковская, О. А. Жульковский, А. Д. Журавский
Keywords
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