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This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic and mathematical capability of the digital computer can be enhanced in a quite natural way. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties of these models are extracted into an axiomatic approach which leads to a general theory of computer arithmetic. Detailed methods and circuits for the implementation of this advanced computer arithmetic on digital computers are developed in part two of the book. Part three then illustrates by a number of sample applications how this extended computer arithmetic can be used to compute highly accurate and mathematically verified results. The book can be used as a high-level undergraduate textbook but also as reference work for research in computer arithmetic and applied mathematics.

Computer arithmetic. --- Computer arithmetic and logic units. --- Floating-point arithmetic. --- Computer arithmetic --- Arithmetic and logic units, Computer --- Electronic digital computers --- Digital arithmetic --- Digital computer arithmetic --- Arithmetic --- Computer architecture --- Circuits

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Scientific computing with automatic result verification

Computer science --- Numerical calculations --- Numerical analysis --- Algorithms. --- Verification. --- Computer programs. --- Algorism --- Algebra --- Arithmetic --- Verification of numerical calculations --- Foundations

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Numerical analysis --- Computer. Automation --- ALGEBRA --- Computer arithmetic --- Data processing --- data processing --- Algebra --- -Computer arithmetic --- -519.6 --- 681.3 *G10 --- 681.3*B2 --- 681.3*G1 --- Mathematical analysis --- Digital arithmetic --- Digital computer arithmetic --- Arithmetic --- Computer architecture --- Mathematics --- Computational mathematics. Numerical analysis. Computer programming --- Computerwetenschap--?*G10 --- Arithmetic and logic structures--(hardware) --- 681.3*G1 Numerical analysis --- 681.3*B2 Arithmetic and logic structures--(hardware) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.6 --- Information (Traitement automatique de l'). Sciences. --- Numerical analysis - Data processing. --- Algebra - Data processing. --- Computer arithmetic. --- Elektronische informatieverwerking. Wetenschap. --- Numerical analysis - Data processing --- ALGEBRA - data processing

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Numerical analysis --- Computer science --- 519.6 --- 681.3 *G10 --- 681.3*B2 --- 681.3*G1 --- Computational mathematics. Numerical analysis. Computer programming --- Computerwetenschap--?*G10 --- Arithmetic and logic structures--(hardware) --- 681.3*G1 Numerical analysis --- 681.3*B2 Arithmetic and logic structures--(hardware) --- 519.6 Computational mathematics. Numerical analysis. Computer programming

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Numerical analysis --- Error analysis (Mathematics) --- #KVIV:BB --- 519.6 --- 681.3 *G10 --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Errors, Theory of --- Instrumental variables (Statistics) --- Mathematical statistics --- Statistics --- Mathematical analysis --- Computerwetenschap--?*G10