This paper presents principles and preferences for the implementation of computer arithmetic and ideals for the arithmetic facilities in future programming languages. the implementation principles and preferences are for the current approaches to the design of arithmetic units. The ideals are for the long term development of programming languages, with the hope that arithmetic units will be bui...

For difference equations with bounded, non-periodic solutions, the natural measure of the equation is a useful descriptor of the geometry of the solution. When it exists, it catalogs the density of typical bounded solutions of the equation, and can be used to characterize its dynamics. By their nature, non-periodic solutions evade easy description. Computer methods are usually needed. In case o...

Speaker: Jennifer Balakrishnan (Boston University) and Jan Tuitman (KU Leuven) Title: Computing Coleman integrals I and II Abstract: We’ll give a survey of explicit Coleman integration on curves via recent algorithms in point-counting and present some applications of Coleman integrals in arithmetic geometry. We’ll also describe some new computations on curves of genus 3. We’ll give a survey of ...

The paper deals with efficient hardware implementation of exact arithmetic. This kind of arithmetic represents the most convenient approach to scientific computing, but the complexity of underlying algorithms and thus the performance issues limit the set of solvable problems. We demonstrate on a particular example of continued logarithms that direct hardware implementation may help to achieve c...

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We define an axiom system for rounded arithmetic to be complete if we can recover from any model of the axioms the exact algebra from whence it came. A complete set of axioms is given for rounded addition and multiplication. In some circles of numerical analysis, there is a deep suspicion that some of the scientific and engineering calculations being done by computer do not correspond to extern...

Computer arithmetic algorithms usually are represented by circuit diagrams which do not seem to be the first choice for algorithms. Rather, this is a consequence of the fact that these algorithms are implemented as circuits in almost all cases. However, it is possible to represent these algorithms in a procedural way, as is shown in this work. A specialized programming language is developed to ...

Parity checking comprises a low-redundancy method for the design of reliable digital systems. While quite effective for detecting single-bit transmission or storage errors, parity encoding has not been widely used for checking the correctness of arithmetic results because parity is not preserved during arithmetic operations and parity prediction requires fairly complex circuits in most cases. W...

The uncertainty in the variables and functions in computer simulations can be quantified by probability distributions and the correlations between the variables. We augment the standard computer arithmetic operations and the interval arithmetic approach to include probability distribution variable (PDV) as a basic data type. Probability distribution variable is a random variable that is usually...

BF-1.1 The idea of this problem is to show how English phrases are translated into logical expressions. (a) f ∧ s. In English, “but” is “and” with an underlying message: The use of “but” in this way often (but not always) indicates surprise. You might say, “The animal is a fish and it lives in the water.” (F ∧W ) Or you might say “The animal is a fish but it lives on dry land.” (F ∧ L) Logic do...