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https://www.cs.colostate.edu/AlphaZ/wiki/
2026-05-16T11:33:11+00:00AlphaZ
https://www.cs.colostate.edu/AlphaZ/wiki/
https://www.cs.colostate.edu/AlphaZ/wiki/lib/tpl/dokuwiki/images/favicon.icotext/html2017-04-19T13:31:43+00:00Anonymous (anonymous@undisclosed.example.com)calculator
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=calculator&rev=1492630303&do=diff
Polyhedral Calculator
This page provides examples of how to use the calculator feature in the AlphaZ system.
The calculator is simply an interface to the underlying polyhedral libraries.
There are a number of commands available in the script interface with prefixtext/html2014-05-30T11:49:53+00:00Anonymous (anonymous@undisclosed.example.com)caveat
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=caveat&rev=1401472193&do=diff
You may have noticed that in the original, mathematical equation at the top of the page, there were bounds on the summation, <latex>$\sum_{k=1}^{i-1}$</latex>. In the Alphabets program we wrote, we did not include these bounds. In this equation, this is safe, for a rather subtle reason (which will be clearer when you know more about Alpha). In general, it is always safe to include these bounds explicitly in your program by making the reduction body a RestrictExpression to explicitly specify t…text/html2017-04-19T14:15:52+00:00Anonymous (anonymous@undisclosed.example.com)change_of_basis
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=change_of_basis&rev=1492632952&do=diff
Change of Basis
Change of basis is a useful transformation in a lot of aspect. This page shows how to use command CoB to apply change of basis on a program.
Usage
Here is the usage for CoB:
The meaning for each parameters are:
* program: the program you are processing.text/html2017-04-19T14:11:20+00:00Anonymous (anonymous@undisclosed.example.com)check_program
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=check_program&rev=1492632680&do=diff
Check Program
This tutorial will explain 'Check Program' utility that checks the correctness of an Alphabets program through static analysis. The rules 'Check Program' uses are described in “Hierarchical Static Analysis of Structured Systems of Affine Recurrence Equationstext/html2014-05-30T11:49:53+00:00Anonymous (anonymous@undisclosed.example.com)code_gen_options
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=code_gen_options&rev=1401472193&do=diff
There are a number of options to the AlphaZ ScheduledC code generator, for example, we can choose to allocate a multi-dimensional array as a one dimensional array or not.
To configure options to be used by the code generator, an instance of an CodeGenOptions object must be created first using the following commands.text/html2022-09-15T21:27:24+00:00Anonymous (anonymous@undisclosed.example.com)command_line_alphaz
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=command_line_alphaz&rev=1663298844&do=diff
Running AlphaZ from Command Line
Although AlphaZ is mainly designed to be used from Eclipse, it is sometime desirable to run the compiler scripts from command line.
#!/bin/bash
ECLIPSE=/s/chopin/h/proj/AlphaZ/BinTree/eclipse-alphaz-bundle/eclipse/eclipse
SCRIPT=basicTest.cs
WORKSPACE=./workspace
${ECLIPSE} -application fr.irisa.r2d2.gecos.framework.compiler -c ${SCRIPT} -data ${WORKSPACE} -noSplashtext/html2023-06-01T17:01:48+00:00Anonymous (anonymous@undisclosed.example.com)eclipse_setup
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=eclipse_setup&rev=1685660508&do=diff
AlphaZ has been only tested on 64 bit Linux and MacOS. There are several options that can be used to get a working eclipse instance with AlphaZ installed.
Option 1 - Eclipse Setup on CS Department Machines
You must be a CSU student with access to the CS deparment machines to do this. An eclipse environment with all necessary plug-ins is available in the AlphaZ project directory. Run the following in a bash terminal to add the AlphaZ project directory to your path:text/html2017-11-14T07:50:52+00:00Anonymous (anonymous@undisclosed.example.com)normalize
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=normalize&rev=1510671052&do=diff
Normalize
Sometimes, the expressions in an alphabets program is not written in the normal form as it is defined, which makes the program hard to read and understand. Nomalize is used to normalize the expressions in a program to the defined normal form. This page shows how to use Normalize to normalize a program.$e.f \Rightarrow e, $$f(z)=z$$(e_{1} \oplus e_{2}).f \Rightarrow (e_{1}.f) \oplus (e_{2}.f)$$(D:e_{1})\oplus e_{2} \Rightarrow D:(e_{1} \oplus e_{2})$$e_{1}\oplus (D: e_{2}) \Rightarrow …text/html2014-05-30T11:49:53+00:00Anonymous (anonymous@undisclosed.example.com)polymodel_verifier
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=polymodel_verifier&rev=1401472193&do=diff
Verifier
Bundle Setup
I have prepared a bundle including Eclipse itself:
<http://www.cs.colostate.edu/AlphaZ/bundles/eclipse-verifier-bundle-linux64.tar.gz>
The bundle is based on Eclipse Classic 3.7.1.
The above bundle contains all necessary plug-ins to use the following project:
<http://www.cs.colostate.edu/AlphaZ/bundles/org.polymodel.verifier.IF.ada.tar>
This verifier.IF.ada project contains examples to use the verifier. For trying out the verifier, I suggest that you download the bun…text/html2014-05-30T11:49:53+00:00Anonymous (anonymous@undisclosed.example.com)publication
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=publication&rev=1401472193&do=diff
Related Publications
International Conference/Workshop
* AlphaZ: A System for Design Space Exploration in the Polyhedral Model, Tomofumi Yuki, Gautam Gupta, DaeGon Kim, Tanveer Pathan, and Sanjay Rajopadhye, 25th International Workshop on Languages and Compilers for Parallel Computingtext/html2017-04-19T13:31:43+00:00Anonymous (anonymous@undisclosed.example.com)reduction_tutorial
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=reduction_tutorial&rev=1492630303&do=diff
Reduction Transformations
This tutorial covers transformations on reductions. Reductions are first-class expressions in Alphabets, enabling compact specification of computations as well as powerful optimizations. In particular, we will see an extremely powerful transformation that allows us to change the asymptotic complexity of the program. In addition, we will also see two other transformations that may be necessary pre-processing in order to enable simplifying reductions.text/html2020-06-10T07:34:44+00:00Anonymous (anonymous@undisclosed.example.com)schedule_code_generator
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=schedule_code_generator&rev=1591796084&do=diff
Schedule Code Generator
Given an affine system and a target mapping, this page shows how to generate the scheduled code based on the given target mapping.
Usage
For the Alphabets program for matrix product.
The following commands will generate the scheduled code based on the given target mapping.text/html2017-04-19T13:31:43+00:00Anonymous (anonymous@undisclosed.example.com)schedule_code_generator_for_code_with_subsystem
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=schedule_code_generator_for_code_with_subsystem&rev=1492630303&do=diff
Schedule Code Generator for SubSystem
Given an affine system with subsystems/useEquations, this page shows how to specify the targetmapping for the system and generate the code.
Matrix Multiplication with subsystem
The following code is the alpha program for matrix matrix multiplication with dot-product subsystem.text/html2017-04-19T13:31:43+00:00Anonymous (anonymous@undisclosed.example.com)schedulers
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=schedulers&rev=1492630303&do=diff
Schedulers
Thanks to ISL, we AlphaZ now have two schedulers. Multi-dimensional farkas scheduler by Paul Feautrier, and PLuTo scheduling by Uday Bondhugula. For details of the schedulers, refer to the corresponding articles.
@article{feautrier1992some,
title={Some efficient solutions to the affine scheduling problem. part II. multidimensional time},
author={Feautrier, P.},
journal={International Journal of Parallel Programming},
volume={21},
number={6},
pages={389--420},
year={1992…text/html2014-05-30T11:49:53+00:00Anonymous (anonymous@undisclosed.example.com)source_access
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=source_access&rev=1401472193&do=diff
AlphaZ Repository
AlphaZ system is now designed based on eclipse plug-in projects for better collaboration with CAIRN group in IRISA, France. We currently have two repositories hosting different parts of the system, based on where it was initially developed.text/html2024-09-11T09:30:37+00:00Anonymous (anonymous@undisclosed.example.com)start
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=start&rev=1726068637&do=diff
AlphaZ Wiki
This wiki is intended to serve as the user manual of AlphaZ. If you are an AlphaZ developer, you should refer to the
AlphaZ Developers wiki
Introduction
AlphaZ is an open source tool-set for program analysis, transformation and parallelization in the Polyhedral Equational Model. It is being developed by the Mélange group (text/html2015-03-06T09:30:48+00:00Anonymous (anonymous@undisclosed.example.com)target_mapping
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=target_mapping&rev=1425659448&do=diff
Target Mapping
To generate scheduled code from an Alphabets program, the code generator in AlphaZ needs some information about (i) the schedule, the (ii) processor allocation, (iii) the memory allocation and (iv) a tiling. Some of these are optional. The target mapping is a unified manner to specify these. This tutorial will cover how to specify the first three: the Space-Time mapping (i and ii) and the Memory mapping (iii).text/html2017-04-19T13:31:43+00:00Anonymous (anonymous@undisclosed.example.com)tiled_code_generator_dtiler
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=tiled_code_generator_dtiler&rev=1492630303&do=diff
Tiled Code Generator
Tiling is an important program transformation that is used to improve data locality and parallelization granularity. We provide a tiled code generator that produces tiled code with wavefront parallelization supported for the shared memory machine.text/html2023-05-30T07:37:55+00:00Anonymous (anonymous@undisclosed.example.com)tutorial_external_function
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=tutorial_external_function&rev=1685453875&do=diff
In this tutorial, how to call functions that are not written or cannot be written in Alphabets is covered.
Using External Functions
In Alphabets, prototypes of external functions can be declared at the beginning of an Alphabets file.
These declared functions can be used like other point-wise operators with variable inputs in Alphabets (MultiArgExpression).text/html2024-09-26T07:56:31+00:00Anonymous (anonymous@undisclosed.example.com)tutorial_forward_substitution
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=tutorial_forward_substitution&rev=1727358991&do=diff
Getting started with Alpha and AlphaZ
Alpha is a polyhedral equational language, and AlphaZ is its “IDE:” tools to read, write, edit, and analyze Alpha Programs, and also to compile them to executable code.
Your first Alpha program (not hello world)text/html2019-04-05T09:02:49+00:00Anonymous (anonymous@undisclosed.example.com)tutorial_lud
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=tutorial_lud&rev=1554476569&do=diff
In this tutorial, we write an Alphabets (or Alpha, for now the two are synonymous) program, starting from a mathematical equation for LU decomposition. Then we will generate code to execute the alpha program, and test the generated code for correctness.$$
U_{i,j}=\begin{cases}
1=i\le j & A_{i,j}\\
1<i\le j & A_{i,j}-\sum_{k=1}^{i-1}L_{i,k}U_{k,j}
\end{cases}\\
L_{i,j}=\begin{cases}
1 = i\le j & \frac{A_{i,j}}{U_{j,j}}\\
1< i\le j & \frac{1}{U_{j,j}}(A_{i,j}-\sum_{k=1}^{j-1}L_{i,k}U_{k,j})
…text/html2017-04-19T13:31:43+00:00Anonymous (anonymous@undisclosed.example.com)tutorial_subsystem
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=tutorial_subsystem&rev=1492630303&do=diff
SubSystem in Alpha
In this tutorial, we will present how to write structured alpha programs with subsystems, and we will present the associated transformations.
Syntax of Use Equation (without extension domain)
Let us assume that we want to compute the mean of the values of a vector. It is feasible through the following Alpha system:text/html2014-05-30T11:49:53+00:00Anonymous (anonymous@undisclosed.example.com)verifier
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=verifier&rev=1401472193&do=diff
Verifier
Given an affine system and a target mapping. The verifier checks the legality of mapping.
Usage
public VerifyTargetMapping(Program program, String system, String verbose)
“NONE”, “MIN” or “MAX” should be passed for verbosetext/html2014-05-30T11:49:53+00:00Anonymous (anonymous@undisclosed.example.com)wiki_editing_title
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=wiki_editing_title&rev=1401472193&do=diff
wiki editing contenttext/html2014-05-30T11:49:53+00:00Anonymous (anonymous@undisclosed.example.com)wrapper_mflops
https://www.cs.colostate.edu/AlphaZ/wiki/doku.php?id=wrapper_mflops&rev=1401472193&do=diff
In the wrapper code generated by AlphaZ, there is a block that looks like the following.
//MFLOPS computation
{
double totalFLOP = 0.0;
/***PROTECTED REGION ID(systemName_MLOPS) ENABLED START***/
//add code to compute the total number of MFLOP here
/***PROTECTED REGION END***/
//only computes and prints MFLOPS when code is added above
if (totalFLOP > 0.0) {
…