E-methodHW – Polynomial and Rational Function Approximations for FPGAs

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Project Overview

This project proposes an automatic method for the evaluation of functions via polynomial or rational approximations and its hardware implementation, on FPGAs.

These approximations are evaluated using Ercegovac's iterative E-method ^{1 2} adapted for FPGA implementation.

The polynomial and rational function coefficients are optimized such that they satisfy the constraints of the E-method.

If you would like to find more technical details, as well as comparisons with other tools that offer hardware function approximations, have a look in the research report. You can also have a look at the slides of the presentation that Silviu-Ioan Filip gave at ARITH25, presenting the project.

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1: M. D. Ercegovac, “A general method for evaluation of functions and computation in a digital computer,” Ph.D. dissertation, Dept. of Computer Science, University of Illinois, Urbana-Champaign, IL, 1975.

2: M. D. Ercegovac, “A general hardware-oriented method for evaluation of functions and computations in a digital computer,” IEEE Trans. Comput., vol. C-26, no. 7, pp. 667–680, 1977.

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Installation Instructions

E-methodHW depends on the efrac library and on FloPoCo. In turn, efrac depends on: gmp, mpfr, mpreal, fplll, eigen and qsopt_ex. You can follow instructions on the respective websites in order to install them on your system. FloPoCo has a pretty extensive list of dependencies, that you can check on the project's page. Alternatively, you can use their one-line install to get everything ready (you can leave out the download and install of the actual library, as everything required is provided in this repository). Alternatively (and hoping you have one of the supported distributions) here is the required shell command:

sudo apt-get install g++ libgmp3-dev libmpfr-dev libfplll-dev libxml2-dev bison libmpfi-dev flex cmake libboost-all-dev libgsl0-dev && wget https://gforge.inria.fr/frs/download.php/33151/sollya-4.1.tar.gz && tar xzf sollya-4.1.tar.gz && cd sollya-4.1/ && ./configure && make -j4 && sudo make install

In order to use E-MethodHW you need to start by either cloning (follow the instructions at the top of this page) or downloading and then unpacking the archive. Asuming that the extracted project is in the emethod directory, building the project can be done using the following commands:

cd emethod
cd main
cmake .
make all

There are several build options, that can be passed directly to cmake.

-DCFG_TYPE=Release|Debug

set by default to Release, will generate debug information and show debug messages during compilation if set to Debug.

-DCFG_FLOPOCO=Lib|LibExec

set by default to Lib, allows building FloPoCo as either library only, or library and executable (useful for comparing the performance of E-methodHW, as described in the research report).

If you would like to remove the files generated during build or subsequent runs of emethodHW, type:

make clean-all

If you would like to remove the files generated during the build of emethodHW type:

make clean-cmake-files

If you would like to remove only the files generated during the execution of emethodHW, type:

make clean-run-files

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Usage

Passing parameters

There are several ways of passing paremeters to emethodHW. In decreasing order of their priority, they are:

1. command line
2. default values
3. configuration file

Parameters on the command line are passed as:

--<parameter_name>=<value>

The exact format of <value>depends on its actual format (for example, a string is specified between single or double quotes).

Parameters in the configuration file are passed as:

<parameter_name>=value

each on an individual line. You can insert lines that start with # in orderto separate the parameters into groups.

For details on the default values, pull up the help, by typing:

emethod --help-all

, or have a look at the CommandLineParser.cpp file.

If no parameters are provided, emethodHW is configured to run Example 1 from the research report.

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