Trans-Floating-Point Arithmetic Removes Nine Quadrillion Redundancies From 64-bit IEEE 754 Floating-Point Arithmetic

@inproceedings{Anderson2014TransFloatingPointAR,
  title={Trans-Floating-Point Arithmetic Removes Nine Quadrillion Redundancies From 64-bit IEEE 754 Floating-Point Arithmetic},
  author={James Anderson},
  year={2014}
}
IEEE 754 floating-point arithmetic is widely used in modern, general-purpose computers. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. Modifying the IEEE arithmetic so that it uses transreal arithmetic has a number of advantages. It removes one… Expand
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Evolutionary and Revolutionary Effects of Transcomputation
Perspex Machine VIII: axioms of transreal arithmetic
IEEE Standard for Floating-Point Arithmetic
IEEE Standard for Binary Floating Point Arithmetic