March 11 – 16 , 2018, Dagstuhl Seminar 18111

Loop Optimization


Sebastian Hack (Universität des Saarlandes, DE)
Paul H. J. Kelly (Imperial College London, GB)
Christian Lengauer (Universität Passau, DE)

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Loop optimization is at the heart of effective program optimization – even if the source language is too abstract to contain loop constructs explicitly as, e.g., in a functional style or a domain-specific language. Increasingly, performance goals are not only execution speed, but also throughput, power efficiency or a combination of these and other criteria.

Context. The quick and easy way to optimize a loop nest, still frequently used in practice, is by restructuring the source program, e.g., by permuting, tiling or skewing the loop nest. Beside being laborious and error-prone, this approach favours modifications that can be easily recognized and carried out, but which need not be the most suitable choice. A much better approach is to search automatically for optimization options in a mathematical model of the iteration space, in which all options are equally detectable and the quality of each option can be assessed precisely.

Recently, the polyhedral compilation community has produced a set of robust and powerful libraries that contain a variety of algorithms for the manipulation of Presburger sets, including all standard polyhedral compilation techniques. They can be incorporated in a program analysis to make other compiler optimizations more precise and powerful, like optimizers and code generators for domain-specific languages, or aggressive optimizers for high-performance computing.

Polyhedral loop optimization relies on strict constraints on the structure of the loop nest and may incur a computationally complex program analysis, based on integer linear programming. The optimization problems become much simpler when information at load or run time is available, i.e., the optimization is done just in time. Also, the search for the best optimization can be supported by other techniques, e.g., auto-tuning, machine learning or genetic algorithms. While these techniques are all fully automatic, engineering of software with robust performance characteristics requires programmers to have some level of explicit control over the data distribution and communication costs. However, manually optimized code is far too complicated to maintain. Thus, a major research area concerns the design of tools that allow developers to guide or direct analysis (e.g., via dependence summaries or domain-specific code generation) and optimization (e.g., via directives, sketches and abstractions for schedules and data partitioning).

This seminar. This seminar will foster a major new synergy in loop optimization research. The key unifying idea is to formulate loop optimization as a mathematical problem, by characterizing the optimization space and objectives with respect to a suitable model.

Participants in the seminar will span some of the major different schools of thought in this field.

One such school is focused on reasoning about scheduling and parallelization using a geometric, “polyhedral”, model of iteration spaces which supports powerful tools for measuring parallelism, locality and communication – but which is quite limited in its applicability.

Another major school treats program optimization as program synthesis, for example by equational rewriting, generating a potentially large space of variants which can be pruned with respect to properties like load balance and locality. This approach has flourished in certain application domains, but also suffers from problems with generalization.

A third family of loop optimization approaches tackles program optimization through program generation and symbolic evaluation. Generative approaches, such as explicit staging, support programmers in taking explicit control over implementation details at a high level of abstraction.

The seminar’s goal is to explore the interplay of these various loop optimization techniques and to consolidate a wider research community of model-based loop optimization. Participants will be representatives of the various loop optimization approaches but also representatives of application domains in high-performance computing.

  Creative Commons BY 3.0 DE
  Sebastian Hack, Paul H. J. Kelly, and Christian Lengauer

Related Dagstuhl Seminar


  • Optimization / Scheduling
  • Programming Languages / Compiler
  • Software Engineering


  • Autotuning
  • Dependence analysis
  • Just-in-time (JIT)
  • Loop parallelization
  • Parallel programming
  • Polyhedron model

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