cppposit

Emanuele Ruffaldi Federico Rossi

Implementation of John L. Gustafson Unum Type III aka Posits using C++ Templates. Initial inspiration was the existing C++ https://github.com/libcg/bfp but then we diverged a lot with several features as detailed below.

Features

Overall:

• Posit's total bits from 4 to 64
• storage in larger holding type (always signed in) e.g 12bit in 16bits
• any valid exponent bits size
• support of variant with NaN and signed Infinity (see below)
• implementation of operations expressed over 4 possible levels (see below)
• constexpr whenever possible
• integration with Eigen
• C++17

The library supports many variants of the Posits as controlled by the template parameters:

template <class T,int totalbits, int esbits, class BackendType, PositSpec specs>

• this is a Posit with totalbits size and it is stored in an storage type of class T whose size is at least totalbits.
• totalbits can go from 2 to 63
• esbits is the maximum exponent size in bits. Values from 0 to totalbits-1 are supported
• BackendType is the data type that holds the fractional part during operations (more info about backends here )
• PositSpec is a type used to interpret the value of the represented by the integer $-2^{(nbits-1)}$

enum PositSpec {
	WithNone, /// never consider special numbers. The top value is never present
	WithNan, /// one top Nan (or Nar using posit spec terminology)
	WithNanInfs, /// one top Nan and two signed Infinites (for more float compatibility)
	WithInfs /// one top Nan and two signed Infinites (for more float compatibility)
}; 

Documentation

API and documentation is available here.

Bibliography

cppposit has been extensively used and expanded by the following works:

1. Cococcioni, Marco; Rossi, Federico; Ruffaldi, Emanuele; Saponara, Sergio
   Fast Approximations of Activation Functions in Deep Neural Networks when using Posit Arithmetic
   Sensors, vol. 20(5), 2020

2. Cococcioni, Marco; Rossi, Federico; Ruffaldi, Emanuele; Saponara, Sergio; Dupont de Dinechin, Benoit
   Novel Arithmetics in Deep Neural Networks Signal Processing for Autonomous Driving: Challenges and Opportunities
   IEEE Signal Processing Magazine, vol. 38(1), pp. 97-110, 2021

3. Cococcioni, Marco; Rossi, Federico; Ruffaldi, Emanuele; Saponara, Sergio
   A Lightweight Posit Processing Unit for RISC-V Processors in Deep Neural Network Applications
   IEEE Transactions on Emerging Topics in Computing, vol. (), pp. 1-1, 2021

4. Cococcioni, Marco; Rossi, Federico; Ruffaldi, Emanuele; Saponara, Sergio
   A Fast Approximation of the Hyperbolic Tangent When Using Posit Numbers and Its Application to Deep Neural Networks
   In Applications in Electronics Pervading Industry, Environment and Society, pp. 213--221, 2020

5. Cococcioni, Marco; Rossi, Federico; Ruffaldi, Emanuele; Saponara, Sergio
   Novel Arithmetics to Accelerate Machine Learning Classifiers in Autonomous Driving Applications
   In 2019 26th IEEE International Conference on Electronics, Circuits and Systems (ICECS), pp. 779-782, 2019

6. Cococcioni, Marco; Rossi, Federico; Ruffaldi, Emanuele; Saponara, Sergio
   A Novel Posit-based Fast Approximation of ELU Activation Function for Deep Neural Networks
   In 2020 IEEE International Conference on Smart Computing (SMARTCOMP), pp. 244-246, 2020

7. Cococcioni, Marco; Rossi, Federico; Ruffaldi, Emanuele; Saponara, Sergio
   Small Reals Representations for Deep Learning at the Edge: A Comparison
   In Next Generation Arithmetic, pp. 117--133, 2022

8. Neves, Nuno; Crespo, Luis; Rossi, Federico; Cococcioni, Marco; Saponara, Sergio; Kuehn, Martin; Krueger, Jens; Tomas, Pedro; Roma, Nuno
   An FPGA-based platform to evaluate Posit arithmetic in next-generation processors
   In ISC High Performance (Poster), 2023