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Universal coding of the reals
- Source :
- Proceedings of the Conference for Next Generation Arithmetic.
- Publication Year :
- 2018
- Publisher :
- ACM, 2018.
-
Abstract
- We propose a modular framework for representing the real numbers that generalizes ieee, posits, and related floating-point number systems, and which has its roots in universal codes for the positive integers such as the Elias codes. This framework unifies several known but seemingly unrelated representations within a single schema while also introducing new representations. We particularly focus on variable-length encoding of the binary exponent and on the manner in which fraction bits are mapped to values. Our framework builds upon and shares many of the attractive properties of posits but allows for independent experimentation with exponent codes, fraction mappings, reciprocal closure, rounding modes, handling of under- and overflow, and underlying precision.
- Subjects :
- Discrete mathematics
Floating point
Computer science
Rounding
Binary number
010103 numerical & computational mathematics
02 engineering and technology
01 natural sciences
IEEE floating point
020202 computer hardware & architecture
0202 electrical engineering, electronic engineering, information engineering
Exponent
0101 mathematics
Round-off error
Reciprocal
Real number
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Proceedings of the Conference for Next Generation Arithmetic
- Accession number :
- edsair.doi...........c659c89c82b582033e40075968f72e8e