Floating point expansion is a technique for implementing multiple precision using a processor's oating point unit instead of its integer unit. Research on this subject has arised recently from the observation that the oating point unit becomes a more and more eÆcient part of modern computers. Many simple arithmetic operators and some very useful geometric operators have already been presented o...

With the growing popularity of decimal computer arithmetic in scientific, commercial, financial and Internet-based applications, hardware realisation of decimal arithmetic algorithms is gaining more importance. Hardware decimal arithmetic units now serve as an integral part of some recently commercialised general purpose processors, where complex decimal arithmetic operations, such as multiplic...

Symmetric level-index arithmetic was introduced to overcome recognized limitations of oating-point systems, most notably overrow and un-derrow. The original recursive algorithms for arithmetic operations could be parallelized to some extent, particularly when applied to extended sums or products, and a SIMD software implementation of some of these algorithms is described. The main purpose of th...

Examples of the use of interval methods in this connection: 1)A physics problem at Lockheed (ca. 1960): Q: Is the strange behavior of the computer model due to round-off errors? A: After converting the program to run in interval arithmetic with outward rounding, it was determined that round-off error was very small in the original program. Result: the physicist took another look at the model eq...

The SCMFSA computer can prove the correctness of many algorithms. Unfortunately, it cannot prove the correctness of recursive algorithms. For this reason, this article improves the SCMFSA computer and presents a Small Computer Model with PushDown Stack (called SCMPDS for short). In addition to conventional arithmetic and ”goto” instructions, we increase two new instructions such as ”return” and...

The SCMFSA computer can prove the correctness of many algorithms. Unfortunately, it cannot prove the correctness of recursive algorithms. For this reason, this article improves the SCMFSA computer and presents a Small Computer Model with Push-Down Stack (called SCMPDS for short). In addition to conventional arithmetic and ”goto” instructions, we increase two new instructions such as ”return” an...

units (adders, ALUs, multipliers, dividers) are essential to fault-tolerant computer designs. Some researchers based early design schemes for such units on arithmetic residue codes.1 Others proposed parity prediction schemes for the same purpose.2 These schemes compute the output operand’s parity as a function of the operator’s internal carries and of the input operands’ parities. The basic dra...

By Grothedieck's Anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number fields encode all arithmetic information of these curves. The goal of this paper is to develope and arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing th...

This research's objective was finding out how employee satisfaction and workplace discipline levels impacted productivity in the Benowo District of Surabaya. Descriptive quantitative research methodology applied this study. there were 34 people chosen randomly as population study, which is 65% total used a sample. In questionnaire collecting data. study multiple linear regression analysis techn...