Hardware Posit Arithmetic Units

This project contains hardware units required for performing floating-point arithmetic operations on numbers represented in the Unum Type-III Posit standard. The parameterized modules have been described in Chisel and can generate synthesizable RTL for posits of any size.

DISCLAIMER: These units are works in progress and are not completely free of bugs or fully optimized.

Technical Report

1. CARRV2020 Paper
2. CARRV2020 Presentation

About Posit Arithmetic

Universal Numbers, or unums, are a collection of number systems which features better efficiency and mathematically correct arithmetic properties compared to the IEEE-754 floating-point standard. Unums are capable of expressing real numbers and ranges of real numbers. The newest version Unum Type-III called Posits is a hardware-friendly representation designed as a drop-in replacement for IEEE floats.

Posits behave much like a floating-point number of fixed size, rounding to the nearest expressible value if the result of a calculation is not expressible exactly. It offers more accuracy, and a larger dynamic range than IEEE floats with the same number of bits. Posit arithmetic tries to resolve the short-comings of IEEE floats using a dynamic representation that minimizes unusable representations and exceptional cases.

For more information about Universal numbers and Posit arithmetic and to follow community discussions:

Posit Hub
Unum-computing Google group

Unit Testing

The posit arithmetic modules have been unit tested using Chisel IO testers. For better coverage a random test generator is also available enabled by the universal C++ template library. The test generator supplies tests to the hardware units which are simulated using verilator.

Prerequisites:

• Install cmake(version 3.14 or later). Refer to https://cmake.org/download/ for installation.
• Install sbt. Refer to https://www.scala-sbt.org/download.html
• Install verilator. On MacOS you can install it using brew install verilator. Refer to https://www.veripool.org/projects/verilator/wiki/Installing

To test the units using verilator:

$ git clone https://github.com/thoughtworks/hardposit-chisel3
$ cd hardposit-chisel3
$ git submodule update --init --recursive
$ make

To test the units using chiseltest:

$ sbt test

Contributions

We are working towards a complete posit implementation including support for quire and all the fused operations mandated by the posit arithmetic standard and optimizing the existing units. Feel free to open an issue or pull request if you find any bugs or possible improvements in the design.

Attribution

If used for research, please cite by the technical report

@inproceedings{ArunkumarM2020PERCPE,
  title={PERC: Posit Enhanced Rocket Chip},
  author={V ArunkumarM. and Sai Ganesh Bhairathi and Harshal G. Hayatnagarkar},
  year={2020},
  url={https://api.semanticscholar.org/CorpusID:221837450}
}