Name
Abstract | ||
|---|---|---|
Recently proposed real-number representations like Posits and Elias codes provide attractive alternatives to IEEE floating point for representing real numbers in science and engineering applications. Many of these applications represent fields on structured grids that exhibit smoothness, where adjacent scalar values are similar and often accessed together in stencil or vector computations. This similarity results in redundancy in representation, where several leading bits in the representation of adjacent values are shared. We propose a generalization of scalar “universal codes” to small, multidimensional blocks of values that exploit their similarity and underlying dimensionality. Drawing upon ideas from multimedia and floating-point compression, our approach combines a decorrelating transform with adaptive, error-optimal interleaving of coefficient bits, which allows increasing accuracy per bit stored by orders of magnitude. Our solution accommodates both a fixed-length representation of blocks—facilitating random access—and variable-length storage to within a user-prescribed tolerance—e.g., for I/O, communication, and streaming computations. Our approach generalizes universal coding of the reals to vectors and tensors, and is straightforward to implement for several known number systems by extending a previously published framework for universal coding based on simple refinement rules.
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Year | DOI | Venue |
|---|---|---|
2022 | 10.1007/978-3-031-09779-9_5 | Next Generation Arithmetic |
Keywords | DocType | ISSN |
Number representations, Floating point, Universal coding, Data compression, Decorrelating transform, Vector quantization | Conference | 0302-9743 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Peter Lindstrom | 1 | 1838 | 103.19 |