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Lightweight Abstraction for Mathematical Computation in Java. Pavel Bourdykine and Stephen M. Watt Department of Computer Science Western University London Ontario, Canada. CASC 2012 Maribor, Slovenia 3-6 September 2012. The Context.

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lightweight abstraction for mathematical computation in java

Lightweight Abstraction for Mathematical Computation in Java

PavelBourdykine and Stephen M. Watt

Department of Computer ScienceWestern University London Ontario, Canada

CASC 2012

Maribor, Slovenia

3-6 September 2012

the context
The Context
  • Modern programming languages allow the creation of new abstractions
    • Hide implementation details
    • Eliminate programming errors
    • Allow future changes

Z/5Zis different from int

Z/5Z [x]is different from int[ ]

the problem
The Problem
  • In the popular scientific programming languages, these mechanisms aren’t good enough.
  • In C++, typedef doesn’t create a distinct type.
  • In Java, adding a class abstraction is very costly.
the problem1
The Problem
  • In symbolic mathematical computing,we often have a great many small values.
  • E.g.
    • Poly coeffs in Z mod small prime
    • Packed exponent vectors
  • Extra storage allocation.Several 100% overhead.
the problem2
The Problem
  • So libraries writers cheat….
  • Compromise abstractions….
  • Circumvent the system ….
  • The standardJava libraries use intand long values to represent
    • Colours, Layout strategies, Border types, etc

instead of abstract types.

  • I.e. language features aren’t good enough.
swing undermining abstraction
Swing, undermining abstraction

static Integers representing different properties

ints representing different parameters

swing undermining abstraction1
Swing, undermining abstraction

Would like to DISTINGUISH between layer and position!

legal, but does not necessarily make sense

same arguments, different meanings

  • Machine-supported data types, such as single- and double-word integers and floating point numbers are primitive types in Java, and specially handled.
    • No storage allocation
    • No “object” overhead (synchronization, etc)
  • User-defined types must be classes inheriting from “Object”, with all the associated overhead.

Primitive type:

Problem multiplies with vectors of these things.

  • Use the Java type system for correctness,then
  • Compile using primitive types.
approach objectives
Approach: Objectives
  • Combine type-safety and low cost
  • Improve performance without crippling safety and expressive power
  • It is about opacity
  • Framework for a straight forward construction
    • easy to use
    • noticeable benefits
approach practice
Approach: Practice
  • Want: objects that perform like primitive types
    • combine the two!
  • Allow class derivation, inheritance, virtualization
    • i.e. object properties
    • WITHOUT the heavy overhead
  • Want to avoid allocation but keep the type safety
  • Works with ANY underlying type!
  • This layer of abstraction does not require its own inheritance structure!
what we would like
What we would like

But achieve this without losing performance and rewriting library functions!

new objects

method arguments no longer ambiguous

approach rules and restrictions
Approach: Rules and Restrictions
  • To keep object properties need to
    • keep representation field protected
    • follow Object-Oriented guidelines

Result: Type-check the objects by name

  • To boost performance and eliminate overhead
    • keep constructor(s) private
    • make methods public static

Result: Implement using underlying type

approach rules and restrictions1
Approach: Rules and Restrictions


  • Rule 1Object must have a single protected field of the underlying type, unless it is a subclass of an opaque type (and then must have no fields).
  • Rule 2Any object constructors must be declared private.
  • Rule 3All methods accessing or modifying the underlying type field representation must be declared static.
approach implementation
Approach: Implementation
  • Annotate opaque classes
    • @Opaque(“type”) annotation
  • Type-check regular objects
  • Convert annotated classes to use underlying type representation
  • Compile the fast versions
  • Converter implemented in Java
  • Building process automated by Ant
code transformation
Code Transformation

Annotated opaque class

code transformation1
Code Transformation

Converted opaque class

compilation process
Compilation Process
  • Annotated code is analyzed and types recorded.
  • All occurrences of opaque types are substituted with the underlying representation.
  • New code is compiled.
  • Process is automated using Ant.
    • Compiles original code for type checking.
    • Backs up the original code, converts it.
    • Calls compiler again on converted code.
  • Test performance in terms of execution speed & memory use
  • Test a variety of uses and declarations
    • cover a wide range of possible applications
  • Measure:

regular code


opaque annotated code


converted code

performance example i
Performance: Example I

Usual Definition:


performance example i1
Performance: Example I

Opaque Definition:


performance example i time
Performance: Example I (time)
  • Opaque types execute about twice as fast
performance example i space
Performance: Example I (space)
  • Opaque types are able to reside entirely on the stack, i.e. no allocation is needed
performance example ii2
Performance: Example II

Regular class usage:

Opaque class usage:

performance example ii time
Performance: Example II (time)
  • Opaque objects execute 12-15 times faster
performance example ii space
Performance: Example II (space)
  • Even before conversion to underlying type opaque types use 10-12 times less memory
performance example ii4
Performance: Example II

Converted opaque class:

performance example ii time1
Performance: Example II (time)
  • Converted (to long[]) opaque types execute 20-25 times faster
performance example ii space1
Performance: Example II (space)
  • Converted (to long[]) opaque types use over 15 times less memory
  • Successfully implemented structures that are type safe and perform as machine types.
  • Code conversion and build process are automated.
  • Performance is well worth the restrictions.
  • Sufficient for computer algebra.

Performance – native levels achieved. Safety – maintained.

future work
Future work
  • Implement Java generics
    • Cover all Java language features
  • Algebra library using opaque types
  • Native implementation?