“Beating Floating Point at Its Own Game: Posit Arithmetic”, 2017-07-23 (; backlinks):
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 substantially 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.
[Keywords: computer arithmetic, energy-efficient computing, floating point, posits, LINPACK⁺, linear algebra, neural networks, unum computing, valid arithmetic]
…Type II unums have many ideal mathematical properties, but rely on table look-up for most operations. If they have n bits of precision, there are (in the worst case) 22n table entries for 2-argument functions, though symmetries and other tricks usually reduce that to a more manageable size. Table size limits the scalability of this ultra-fast format to about 20 bits or less, for current memory technology. Type II unums are also are much less amenable to fused operations. These drawbacks motivated a search for a format that would keep many of the merits of Type II unums, but be “hardware friendly”, that is, computable using existing float-like logic.