Traditional numerical methods for polynomial root computation are fast but they sometimes return wrong results. Algorithms from computer algebra, on the other hand, guarantee correctness but tend to require long computing times. The computing time can, however, be dramatically reduced if exact arithmetic is carefully replaced by floating point arithmetic and if, moreover, ways are found to empl...

This paper provides algorithms in order to solve an interval implicit function of the Poincaré map generated by a continuous piecewise linear (CPWL) vector field, with the use of interval arithmetic. The algorithms are implemented with the use of MAT LAB and INT LAB. We present an application to verification of canards in two-dimensional CPWL vector field appearing in nonlinear piecewise linear...

This paper proposes a new approach for proving arithmetic correctness of data paths in System-on-Chip modules. It complements existing techniques which are, for reasons of complexity, restricted to verifying only the control behavior. The circuit is modeled at the arithmetic bit level (ABL) so that our approach is well adapted to current industrial design styles for high performance data paths....

ÐTraditional computer systems often suffer from roundoff error and catastrophic cancellation in floating point computations. These systems produce apparently high precision results with little or no indication of the accuracy. This paper presents hardware designs, arithmetic algorithms, and software support for a family of variable-precision, interval arithmetic processors. These processors giv...

This paper describes a general algorithm for finding the commensurator of a non-arithmetic hyperbolic manifold with cusps, and for deciding when two such manifolds are commensurable. The method is based on some elementary observations regarding horosphere packings and canonical cell decompositions. For example, we use this to find the commensurators of all non-arithmetic hyperbolic once-punctur...

This paper describes a semi-dynamic CMOS flip-flop family featuring embedded Threshold Logic functions. First, we describe the new Threshold Logic flipflop concept and circuit operation. Second, we present the concepts of embedded Threshold logic and run-time reprogrammability. Finally, it is proved by Spice simulation results that wide (up to 8 inputs) AND/OR Boolean functions can be embedded ...

We present a general method to compute presentation for any cusped arithmetic hyperbolic lattice $\Gamma$, applying classical result of Macbeath suitable $\Gamma$-invariant horoball cover the corresponding symmetric space. As applications we presentations Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$ $d=1,3,7$ and quaternion PU}(2,1,\mathcal{H})$ with entries in Hurwitz integer ring $\mat...

In recent years, motion recognition has become a hot research topic in the field of computer vision and great worth. Scholars institutions at home abroad have made lot achieved good results. However, results applying technology to dance video are relatively few, mainly because complexity human is high. article, an optimized design scheme for based on image processing proposed. The collected pre...

When multiplying really large integer operands, the GNU Multiple Precision Arithmetic Library uses a method based on the Fast Fourier Transform. To make an algorithm execute quickly on a modern computer, data has to be available in the cache memory. If that is not the case, a large portion of the execution time will be spent accessing the main memory. It might pay off to perform much extra work...

The importance of the Dempster-Shafer theory (DST) for modeling and propagating uncertainty has grown in the recent past. An obstacle for wider application of this theory in industrial practice is the lack of software support for analysts. The few tools available depend on floating point arithmetic and do not consider the inherently interval-based nature of the DST to the full extent. Therefore...