[2] The defining features of the Type I unum format are: For computation with the format, Gustafson proposed using interval arithmetic with a pair of unums, what he called a ubound, providing the guarantee that the resulting interval contains the exact solution.
This set of points is chosen arbitrarily, and arithmetic operations involving them are not performed logically but rather by using a lookup table.
This challenge necessitated the development of the Type III unum, known as the posit, discussed below.
In February 2017, Gustafson officially introduced Type III unums (posits), for fixed floating-point-like values and valids for interval arithmetic.
Compared to IEEE 754 floats of similar size, posits offer a bigger dynamic range and more fraction bits for values with magnitude near 1 (but fewer fraction bits for very large or very small values), and Gustafson claims that they offer better accuracy.
[12][13] Studies[14][15] confirm that for some applications, posits with quire out-perform floats in accuracy.
This makes it very attractive to the current trend in deep learning to minimize the number of bits used.
The two encodings in which all non-sign bits are 0 have special interpretations: Otherwise, the posit value is equal to
Note: 32-bit posit is expected to be sufficient to solve almost all classes of applications[citation needed].
The quire format is a two's complement signed integer, interpreted as a multiple of units of magnitude
[16] Valids are described as a Type III Unum mode that bounds results in a given range.
[28][29] A C++ version[30] with support for any posit sizes combined with any number of exponent bits is available.
Uses induction to prove nbits+1 is correct no known bugs Fully integrated with C/C++ types and automatic conversions.
Ken Mercado Federico Rossi, Emanuele Ruffaldi Clément Guérin Isaac Yonemoto Lombiq Technologies (64bits in progress) Click here for more (RTL for FPGA/ASIC designs) Supports +,-,/,*.
***First ever integration of posits in RISC-V*** (Sugandha Tiwari, Neel Gala, Chester Rebeiro, V.Kamakoti, IIT MADRAS) More info here.
David Mallasén Chris Lomont REX Computing Calligo Tech Applications tested and being made available for seamless adoption www.calligotech.com Jianyu Chen Raul Murillo Jaap Aarts SoftPosit[31] is a software implementation of posits based on Berkeley SoftFloat.