Ulrich W. Kulisch – författare

Computer Arithmetic in Theory and Practice deals with computer arithmetic and the various implementations of the entire arithmetic package on diverse processors, including microprocessors. It illustrates the importance of theoretical development in the sound implementation of arithmetic on computers, and argues that such an implementation requires the establishment of various isomorphisms between different definitions of arithmetic operations. Comprised of seven chapters, this volume begins with an introduction to the theory of computer arithmetic by giving an axiomatic characterization of the essential properties of sets and subsets; complete lattices and complete subnets; screens and roundings; and arithmetic operations. The discussion then turns to the concepts of a ringoid and a vectoid as well as those of ordered or weakly ordered ringoids and vectoids; interval arithmetic; and floating-point arithmetic. The operations in interval spaces are defined by means of semimorphisms. The final chapter shows how to embed the five basic data types (integer, real, complex, real interval, and complex interval) together with the arithmetic operations that are defined for all of these types into existing higher programming languages. This book will be helpful to students and practitioners in the fields of computer science and applied mathematics.

A New Approach to Scientific Computation is a collection of papers delivered at a symposium held at the IBM Thomas J. Watson Research Center on August 3, 1982. The symposium provided a forum for reviewing various aspects of an approach to scientific computation based on a systematic theory of computer arithmetic. Computer demonstration packages for standard problems of numerical mathematics are considered. Comprised of 12 chapters, this volume begins by summarizing an extensive research activity in scientific computation as well as the experience gained through various implementations of a new approach to arithmetic on diverse processors, including even microprocessors. A complete listing of the spaces that occur in numerical computations is presented, followed by a discussion of aspects of traditional computer arithmetic and a new definition of computer arithmetic. The properties of semimorphisms are also considered. Subsequent chapters focus on potential applications of programming packages to standard problems in numerical analysis implemented on a Z80 based minicomputer, with a PASCAL extension called PASCAL-SC as the programming language; methods for solving algebraic problems with high accuracy; and the use of a computer with floating-point arithmetic to obtain guaranteed sharp bounds for the value of an arithmetic expression. An extension of FORTRAN which satisfies contemporary requirements of numerical computation is also described. This book will be helpful to students and practitioners in the fields of computer science and applied mathematics.

The book deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic requires that all computer approximations of arithmetic operations - in particular those in the usual vector and matrix spaces - differ from the correct result by at most one rounding. The implementation of advanced computer arithmetic by fast hardware is examined in the book. The new expanded computational capability is gained at modest cost. It increases both the speed of a computation and the accuracy of the computed result. With it fast multiple precision arithmetic can be easily provided. All this strongly supports the case for implementing advanced computer arithmetic on every CPU. The book also shows that on superscalar processors interval operations can be made as fast as simple floating-point operations with only very modest additional hardware costs.