Posit Arithmetic: Language Implications of a New Real Number Format

The posit data type for representing real-valued numbers on computers was introduced at Stanford in February 2017. It was created as a modern alternative to IEEE 754 Standard floating-point numbers ("floats"), which were designed for 1980s-era computing. Using a mathematical design that stores more information-per-bit, posits can have both higher accuracy and larger dynamic range than floats, yet use less time and energy through greatly-simplified exception handling. They also offer something floats failed to achieve: the ability to guarantee bitwise-identical results for computations involving real numbers. This feature, however, has major implications for compilers and language design. Posits also make practical for the first time the XSC language extensions of Ulrich Kulisch et al. that guarantee correct rounding for basic blocks, a major step forward in sparing programmers from having to become experts in numerical analysis.

Bio:  Dr. John L. Gustafson (www.johngustafson.net) is a Professor in the School of Computing at the National University of Singapore. He is the inventor of several novel forms of computer arithmetic first introduced in his 2015 book, The End of Error: Unum Computing.  He is best known for his 1988 argument showing that parallel processing performance need not be limited by "Amdahl's law," now generally known as Gustafson's law. Previously, he has been Senior Fellow and Chief Product Architect at AMD and a Director of Intel Labs. He is a recipient of the inaugural Gordon Bell Prize and is a Golden Core member of IEEE.