approx: A Library of Approximate Arithmetic Units in Chisel

This repository contains a collection of approximate arithmetic units for use in various digital designs. The units are written in Chisel with tests written for the exact units using ChiselTest. Currently only a selection of adders and multipliers and a simple sequential division unit are included - more designs to come!

When you use this library in a research project, please cite it as:

@misc{damsgaard2022approx,
  title={{approx: A Library of Approximate Arithmetic Units in Chisel}},
  author={Damsgaard, Hans Jakob},
  year={2022},
  howpublished={\url{https://github.com/aproposorg/approx}}}

This README only contains a brief overview of the library's current contents. All units are commented to be reasonably understandable for people with prior knowledge of Chisel and Scala. Refer to the Digital Design with Chisel book for more details on these topics.

Requirements

Utilizing Chisel and ChiselTest, approx requires a suitable installation of Scala. For this purpose, we use the Scala Build Tool (sbt) for which we provide a suitable build script.

Moreover, some tests run too slow in ChiselTest's built-in Treadle simulator, so we have instead decided to run them using Verilator (see e.g., Radix2MultiplierSpec here). Thus, to run all provided tests, one must have a suitable installation of Verilator available. Note that only specific versions of Verilator are officially supported.

This library is tested in Ubuntu 20.04 with Verilator 4.028.

Adders

The approx.addition library contains a vast number of approximate and exact adder designs that are parameterized to be reasonably flexible. The lists below specify which designs are included currently. We gladly accept requests for other designs as issues in this repository.

Exact designs

All exact designs are based on descriptions in Ercegovac and Lang's book on digital arithmetic.

Approximate designs

Beware that some approximate adders (e.g., DualModeRCA, GeAr) do not extend the abstract Adder base class as their IOs do not match those of the basic adder. Almost all designs are purely combinational; only GeAr has an option for adding a register to support flagging errors.

Multipliers

Like above, the approx.multiplication library contains several approximate and exact multiplier designs that are also parameterized. The list below specifies which designs are included currently. In addition to these, the tool also includes a generic compressor tree generator for ASIC, Xilinx 7-Series/UltraScale or Versal FPGA (supported by the primitives in approx.util.Xilinx), and Intel FPGA flows. The generator supports fully exact compression as well as approximation by column or row truncation, OR-based column compression, and miscounting (i.e., inexact compression). Multiple of these approximations can also be applied concurrently.

Exact designs

All exact designs are based on descriptions in Ercegovac and Lang's book on digital arithmetic. Note that some exact multiplier implementations, specifically Radix2Multiplier, Radix4Multiplier, RecursiveMultiplier, and AdaptiveRadix2Multiplier, permit approximation through their arguments.

Approximate designs

Dividers

The approx.division library currently only contains an exact, sequential radix-2 divider. We hope to extend this collection in the future.

Exact designs

Approximate designs

N/A

Accumulators

The approx.accumulation library currently only contains a number of exact, non-pipelined single-lane and parallel accumulators with options for the parallel designs to be approximated with the custom compressor trees from approx.multiplication.comptree. We also hope to extend this collection in the future.

Exact designs

Approximate designs

N/A