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Analysis of Some Strange Behaviors of Floating Point Arithmetic using MATLAB Programs  

Chung, Tae-Sang (중앙대학교 전자전기공학부)
Publication Information
The Transactions of The Korean Institute of Electrical Engineers / v.56, no.2, 2007 , pp. 428-431 More about this Journal
Abstract
A floating-point number system is used to represent a wide range of real numbers using finite number of bits. The standard the IEEE adopted in 1987 divides the range of real numbers into intervals of [$2^E,2^{E+1}$), where E is an Integer represented with finite bits, and defines equally spaced equal counts of discrete numbers in each interval. Since the numbers are defined discretely, not only the number representation itself includes errors but in floating-point arithmetic some strange behaviors are observed which cannot be agreed with the real world arithmetic. In this paper errors with floating-point number representation, those with arithmetic operations, and those due to order of arithmetic operations are analyzed theoretically with help of and verification with the results of some MATLAB program executions.
Keywords
Floating Point Number System; Error Analysis; Rounding; MATLAB;
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