The IEEE 754 Floating point standard [1] specifies a simple (32 bits) and double precision (64 bits). For the FFT block in a DSL modem (DMT based), even 32 bits proves to be too much, and a custom number of bits can be used. This in turn will lead to savings in area and power on the ASIC implementation. Several techniques were considered for reducing the number of bits.

We discuss interval techniques for speeding up the exact evaluation of geometric predicates and describe a C++ implementation of interval arithmetic that is strongly innuenced by the rounding modes of the widely used IEEE 754 standard. Using this approach we engineer an eecient oating point lter for the computation of geometric predicates. We validate our approach experimentally, comparing it w...

We present deep VLA observations of the galaxy clusters Abell 2256 and Abell 754, both of which appear to be in the violent stage of major cluster merger events. The complex nature of Abell 2256 is revealed through radio images which, in addition to the head-tail galaxies, show two extended, irregular, and sharp-edged regions of diffuse radio emission at the cluster periphery (so called radio r...

Under 5 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 690 6.3 5 to 9 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 6.4 10 to 14 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754 6.8 15 to 19 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 890 8.1 20 to 24 years . . . . . . . . . . . . . . . . . . . . ....

H. Swart, A. Kotze, P.A.S. Olivier and J.P. Grobler 1 Department of Biodiversity, University of Limpopo, P/Bag X1106, Sovenga 0272, South Africa 2 Animal Improvement Institute, Agricultural Research Council, P/Bag X2, Irene 0062, South Africa 3 Department of Genetics, University of the Free State, PO Box 339, Bloemfontein 9300, South Africa 4 National Zoological Gardens of South Africa, PO Box ...

A. Kotzé, J.P. Grobler, E. van Marle-Köster, T. Jonker & D.L. Dalton 1 National Zoological Gardens of South Africa, P.O. Box 754, Pretoria 0001, South Africa 2 Department of Genetics, University of the Free State, P.O. Box 339, Bloemfontein 9300, South Africa 3 Department of Animal & Wildlife Sciences, University of Pretoria, Private Bag X20, Hatfield, Pretoria 0028, South Africa 4 Northern Cap...

This development provides a formal model of IEEE-754 floatingpoint arithmetic. This formalization, including formal specification of the standard and proofs of important properties of floating-point arithmetic, forms the foundation for verifying programs with floating-point computation. There is also a code generation setup for floats so that we can execute programs using this formalization in ...