# Finite Precision Number Systems and Arithmetic

@inproceedings{Kornerup2010FinitePN, title={Finite Precision Number Systems and Arithmetic}, author={Peter Kornerup and David W. Matula}, year={2010} }

Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authorsâ€¦Â

## 33 Citations

Mathematical model and implementation of rational processing

- Computer ScienceJ. Comput. Appl. Math.
- 2017

Exact Real Algorithms for Transcendent Functions

- Computer Science2016 3rd International Conference on Information Science and Control Engineering (ICISCE)
- 2016

The exact real computation is therefore a feasible alternative to the floating point computation, at least in the tasks, in which the precision of the results matters.

A FIXED-POINT DIGIT SERIAL SQUARING ALGORITHM USING AN ARBITRARY NUMBER SYSTEM

- Computer Science
- 2012

The algorithm is derived through a generalization of a Vedic technique where any arbitrary integer-valued radix is used and where no constraints are imposed upon the value of the least significant digit of the squarand.

Parallel Implementation of Exact Matrix Computation Using Multiple P-adic Arithmetic

- Mathematics, Computer Science2013 14th ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing
- 2013

Progress is reported on parallel implementation of P-adic arithmetic by means of a multiple modulus rational system related to the Chinese remainder theorem.

New Formats for Computing with Real-Numbers under Round-to-Nearest

- Computer ScienceIEEE Transactions on Computers
- 2016

In this paper, a new family of formats to deal with real number for applications requiring round to nearest is proposed. They are based on shifting the set of exactly represented numbers which areâ€¦

The Exact Real Arithmetical Algorithm in Binary Continued Fractions

- Computer Science2015 IEEE 22nd Symposium on Computer Arithmetic
- 2015

This work considers a number system of binary continued fractions in which this algorithm is computed faster than in the binary signed system, and circumvents the problem of nonredundancy and slow convergence of continued fractions.

Reviewing High-Radix Signed-Digit Adders

- Computer ScienceIEEE Transactions on Computers
- 2015

It is shown that there are no speed advantages in recoding the addends into a higher radix if the radix is a power of 2, but there are significant savings in using standard 4-to-2 adders, even saving half of the operations in multi-operand addition.

Multiplicative Division Employing Independent Factors

- Mathematics, Computer ScienceIEEE Transactions on Computers
- 2015

Specific derivations of the method for IEEE-754 standard binary single and double precision division are developed in detail, and theoretical error bounds are derived to prove correctness for obtaining properly rounded single precision quotients by rounding the product of these four factors.

A Fixed-Point Squaring Algorithm Using an Implicit Arbitrary Radix Number System

- Computer ScienceIEEE Journal on Emerging and Selected Topics in Circuits and Systems
- 2016

The squarer presented here can be considered a multiple-valued logic (MVL) digit-serial architecture and allows for technologies based on any radix of two or greater to be used, including emerging technologies, thus yielding a true multiple- valued logic squaring circuit.

Implementation of Novel High Radix Multiplier Using KOGGE Stone Adder

- Computer Science
- 2015

It is shown that there are no speed advantages in recoding the addends into a higher radix if the radix is a power of 2, but there are significant savings in using standard 4-to-2 adders, even saving half of the operations in multi-operand addition.