Beating Floating Point at its Own Game: Posit Arithmetic
By John L. Gustafson, Isaac T. Yonemoto. Supercomputing Frontiers and Innovations, 2017
425 citations recorded by the source corpus.
A new data type called a posit is designed as a direct drop-in replacement for IEEE Standard 754 floating-point numbers (floats). Unlike earlier forms of universal number (unum) arithmetic, posits do not require interval arithmetic or variable size operands; like floats, they round if an answer is inexact. However, they provide compelling advantages over floats, including larger dynamic range, higher accuracy, better closure, bitwise identical results across systems, simpler hardware, and simpler exception handling. Posits never overflow to infinity or underflow to zero, and “Not-a-Number” (NaN) indicates an action instead of a bit pattern. A posit processing unit takes less circuitry than an IEEE float FPU. With lower power use and smaller silicon footprint, the posit operations per second (POPS) supported by a chip can be significantly higher than the FLOPS using similar hardware resources. GPU accelerators and Deep Learning processors, in particular, can do more per watt and per dollar with posits, yet deliver superior answer quality. A comprehensive series of benchmarks compares floats and posits for decimals of accuracy produced for a set precision. Low precision posits provide a better solution than “approximate computing” methods that try to tolerate decreased answer quality. High precision posits provide more correct decimals than floats of the same size; in some cases, a 32-bit posit may safely replace a 64-bit float . In other words, posits beat floats at their own game.
Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Hardware and Architecture
View Paper: https://www.semanticscholar.org/paper/bebecf201199cb10333fb8ed673c407cfa6e5a8e
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Citations in the corpus
- Rethinking floating point for deep learning (2018, methodology): “Significant inspiration for our work is found in logarithmic number systems (LNS) [2] and the work of Miyashita et al. [24] that finds logarithmic quantizers better suited to data distributions in NNs, and alternative visions of floating point from Gustafson [11, 12] and Kulisch [19].”