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MSBFirst Digit Serial Arithmetic
, 1995
"... : We develop a formal account of digit serial number representations by describing them as strings from a language. A prefix of a string represents an interval approximating a number by enclosure. Standard online representations are shown to be a special case of the general digit serial representat ..."
Abstract

Cited by 18 (1 self)
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: We develop a formal account of digit serial number representations by describing them as strings from a language. A prefix of a string represents an interval approximating a number by enclosure. Standard online representations are shown to be a special case of the general digit serial representations. Matrices are introduced as representations of intervals and a finitestate transducer is used for mapping strings into intervals. Homographic and bihomographic functions are used for representing basic arithmetic operations on digit serial numbers, and finally a digit serial representation of floating point numbers is introduced. Key Words: Computer Arithmetic, Online Computation, Number Representations, Redundant Digit sets, Continued Fractions, Intervals. Category: B.2 1 Introduction A number is usually represented as a string of digits belonging to some digit set \Sigma . The number representation specifies a function that maps the string to its value. In the context of this pa...
A high radix online arithmetic for credible and accurate computing
 Journal of Universal Computer Science
, 1995
"... Abstract: The result of a simple oatingpoint computation can be in great error, even though no error is signaled, no coding mistakes are in the program, and the computer hardware is functioning correctly. This paper proposes a set of instructions appropriate for a general purpose microprocessor tha ..."
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Cited by 8 (1 self)
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Abstract: The result of a simple oatingpoint computation can be in great error, even though no error is signaled, no coding mistakes are in the program, and the computer hardware is functioning correctly. This paper proposes a set of instructions appropriate for a general purpose microprocessor that can be used to improve the credibility and accuracy of numerical computations. Such instructions provide direct hardware support for monitoring events which may threaten computational integrity, implementing oatingpoint data types of arbitrary precision, and repeating calculations with greater precision. These useful features are obtained by the e cient implementation of high radix online arithmetic. The prevalence of superscalar and VLIW processors makes this approach especially attractive.
Number systems and Digit Serial Arithmetic
, 1997
"... this paper. By introducing an extra termination symbol, which signals that an operand was merely terminated due to its length exceeding some bound, operands can be kept as intervals, representing an imprecise operand. Operands terminated in the ordinary way can be taken to represent exact numbers. T ..."
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Cited by 1 (1 self)
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this paper. By introducing an extra termination symbol, which signals that an operand was merely terminated due to its length exceeding some bound, operands can be kept as intervals, representing an imprecise operand. Operands terminated in the ordinary way can be taken to represent exact numbers. The cube modeling a function of two variables, can be generalized to a hypercube modeling a polyhomographic function of n variables. For n = 3 the function is defined as: