IllinoisIrvine PROMIS Compiler Symbolic Interpreter

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Illinois-Irvine PROMIS CompilerSymbolic
Interpreter

• Hideki Saito
• Nicholas J. Stavrakos
• Constantine D. Polychronopoulos

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Outline

• Symbolic Interpretation
• What is it?
• How does it work?
• Symbolic Kernel
• What can be done during interpretation?
• Interprocedural Aspects
• Performance Issues

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Symbolic Interpretation

• Interprets program to discover properties of the
  program
• Maintains an environment of current execution
  state as each line of code is interpreted.
• Requires a tool to manipulate the symbolic
  values variables take on during interpretation.

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Interpretation Example
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Encoding of Conditional Assignments
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Symbolic Kernel

• Interpreter requires tool to manipulate
• Symbolic expressions
• Expressions containing the truth function t
• This tool is the core of the interpreter
• Needs to be fast
• Needs to be flexible

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Symbolic Kernel

• Supports basic data types
• Supports arbitrary precision data types
• GNU MP (Multiple Precision) library
• Enables cross compilation for systems with
  different intrinsic data types
• (64,128)-bit integers
• Aribitrary precision floating point arithmetic

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Symbol Class Definition
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Uses of Symbolic Interpretation

• SSA Versioning
• Induction Variable Elimination
• Static Performance Prediction
• Range/Type/Constant Propagation
• Symbolic Dependence Analysis
• Strength Reduction

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Symbolic Compiler
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s-SSA Versioning

• Similiar to classic SSA, but constructed during
  interpretation.
• Allows for reevaluation of symbolic expressions
  without reinterpreting entire program.
• Potentially smaller SSA form (less versions) than
  previous SSA algorithms

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s-SSA Construction Example
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Induction Variable Elimination

• Eliminate variables inside loops which contain
  cross-iteration dependencies.
• Computes closed form of variables using loop
  variables or loop constants
• Introduces expensive operations (, /), but
  enables loops to execute in parallel
• Opposite of strength reduction

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Induction Variable Elimination Example
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Strength Reduction

• Replaces expensive instructions ( , / ) with
  less expensive instructions ( , -)
• Introduces cross-iteration dependencies inside
  loops, hence restricting parallelism
• If loop is not parallel, probably better to use
  simple instructions which introduce dependencies,
  than expensive instructions with no dependencies

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Strength Reduction Example
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Static Performance Analysis

• Implemented with the aid of induction variable
  analysis and range propagation
• Compile time estimation of relative sizes of code
  sections
• Guides the ordering of transformations by the
  compiler
• Usefull for scheduling code sections

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Interprocedural Aspects

• When interpreter encounters a function call it
  must evaluate the function call and its effect on
  the current environment
• If function call only has a single call site,
  then entire environment can be transfered to
  function call for evaluation
• If function call has multiple call sites then no
  assumptions can be made about environment when
  evaluating function call

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Interprocedural Symbolic Interpretation
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Performance Issues

• Memory Requirements
• Temporary file storage
• Speed
• No overhead for supporting arbitrary precision
  arithmetic
• User definable values for complexity of
  interpretation

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Conclusion

• Most analysis and transformation techniques can
  use symbolic information (when necessary).
• s-SSA enables retrieval of symbolic expressions
  without reinterpreting entire program.
• Implication IR support required to achieve best
  possible performance from interpreter.