BROOM: A Matrix Language

1
BROOM A Matrix Language

• Chris Tobin
• Michael Weiss
• Gabe Glaser
• Brian Pellegrini

2
Broom Overview and Summary

• A high-level language for manipulating matrices
• Many useful built in matrix operations.
• Ability to define and build more complicated
  functions for specialized analysis of
  information

3
Motivation

• Matrices are universal mathematical constructs
• Learning curve is not as steep
• Specialized use, without extraneous things to
  understand other than what you need it for.
• No need for expensive software

4
Goals

• Intuitive syntax
• High level
• Very portable
• Flexible
• Useful and informative error checking

5
Broom Syntax

• Intuitive
• for ( ) endfor
• Freeform
• whitespace inserted at will
• Smooth built-in matrix operation syntax
• A inv(B) // finds the inverse of B
• Features
• Control flow constructs for, while, if
• Nested logical operators and expressions
• A wide range of built-in functions

6
Built-in Functions

• Many useful built-in function calls
• det
• colswap, rowswap
• inv
• gauss
• appendUD, appendLR
• setCol, setRow
• Too numerous to list22 total

7
Semantics

• Broom features
• Function definitions
• Allow for modularity, power, and reusable code.
• Variable definitions
• Two intuitive mathematical types
• Number
• Matrix
• Scoping rules
• local for functions
• global accessible by all
• All functions call-by-value for simplicity

8
Compiler Components and Composition

• There are 5 main components of BCC, the Broom
  translator
• Lexer
• Parser
• Static Semantics Checker
• W/Symbol Tables
• BroomMatrix.java
• Contains Matrix manipulation code and functions
• Code Generator

9
ANTLR

• The Lexer and Parser were implemented using
  ANTLR.
• ANTLRs AST class was used to create the Abstract
  Syntax Tree and Nodes.
• The Static Semantics Checker was implemented as
  a TreeWalker of the ANTLR AST and maintained
  Symbol Tables for the various scopes.
• Symbol Tables were written as a simple Java class
• Code Generator was also implemented as a
  TreeWalker of ANTLR AST.
• Accumulates a program string as it walks the
  AST and prints string to file upon finishing
  traversal

10
Block Diagram of Compiler
11
Example of Generated Code

• MyProgram.java
• public class MyProgram
• BroomMatrix myMatrix
• public MyProgram()
• float _temp0 (float) 1, (float) 2,
  (float) 3, (float) 4
• myMatrix new BroomMatrix( _temp0)
• public void start()
• float value
• float _temp1 (float) 1, (float) 3,
  (float) 7, (float) 8
• value BroomMatrix.det(BroomMatrix.multiply(myM
  atrix, new BroomMatrix( _temp1)))
• BroomMatrix.printVariable(value)
• BroomMatrix.printVariable(myMatrix)
• public static void main(String args)

• MyProgram.broom
• MyProgram
• global Matrix myMatrix
• myMatrix 1,2
• 3,4
• //function definitions here...
• start()
• Number value
• value det( myMatrix
• 1,3
• 7,8)
• //print the value you got
• value.print()
• //print the global Matrix
• myMatrix.print()
• endstart

12
Output of The Simple Program

• javac MyProgram.java
• java MyProgram
• 26.0
• 1.0 2.0
• 3.0 4.0

13
Error Checking

• Two main types of errors
• Semantic Errors
• Invalid use of logical ops
• Invalid type assignments
• Use of reserved words as variable names, etc.
• Run-Time Errors
• Reference to non-existent index
• Use of improperly formatted matrix.
• Note If de ja vu is experienced something in
  your matrix may have been changed.

14
Example Test Program

• wrongNumColls
• // Test for number of columns errors
• // Author Brian Pellegrini
• // This is supposed to make sure that error
  checking for
• //assignment of matrix values works...it is
  supposed to fail
• // MUA HAHAHHAHAHHAH
• global Matrix A,B
• A 1, 0, 1 0, 1
• B 0, 1 1, 0 , 2
• start()
• print ("If this printed checker didn't work")
• endstart

15
Example Test Results

• BroomProgram did not compile the following
  errors were detected
• Error in global declaration invalid matrix
  specification.
• Expected a row with 3 elements, but got
  2
• Error in global declaration invalid matrix
  specification.
• Expected a row with 2 elements, but got 3
• BROOM compiler found all the errors!
• During testing one has to be careful that errors
  being tested are the only ones present in the
  program
• Inadvertent bugs can cause lots of lost time
  spend debugging ghost bugs

16
Lessons Learned

• Leave no stone unturned
• Need to test every possible error user might
  encounter
• Need to test both errors in users code, and
  errors in generated JAVA code
• Exhaustive testing pays off in the end
• Have someone else try it!
• Have a friend write a program, they might find
  errors that the testing team simply overlooked.