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Semantics of Exact Real Arithmetic
, 1997
"... In this paper, we incorporate a representation of the nonnegative extended real numbers based on the composition of linear fractional transformations with nonnegative integer coefficients into the Programming Language for Computable Functions (PCF) with products. We present two models for the exten ..."
Abstract

Cited by 29 (8 self)
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In this paper, we incorporate a representation of the nonnegative extended real numbers based on the composition of linear fractional transformations with nonnegative integer coefficients into the Programming Language for Computable Functions (PCF) with products. We present two models for the extended language and show that they are computationally adequate with respect to the operational semantics.
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 ..."
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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...
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: