• Corpus ID: 13983888

Symbolic Evaluation of Chains of Recurrencesfor Loop

  title={Symbolic Evaluation of Chains of Recurrencesfor Loop},
  author={OptimizationRobert and A. J. van and EngelenDept},
This paper presents a novel method for loop optimization that exploits symbolic evaluation of chains of recurrences (CRs). The method generalizes loop induction expression recognition, loop parallelization by induction variable substitution, loop strength reduction , and loop invariant expression elimination (code motion). Symbolic diierencing of loops has been extensively studied by Haghighat for these type of transformations. The diierencing method detects generalized loop induction variables… 


Automatic recognition of induction variables and recurrence relations by abstract interpretation
This paper puts forth a systematic method for recognizing recurrence relations automatically, which is easily extensible by the addition of templates, and is able to recognize nested recurrences by the propagation of the closed forms of recurrence from inner loops.
Symbolic Program Analysis and Optimization for Parallelizing Compilers
A program flow analysis framework is proposed for parallelizing compilers where symbolic analysis is used as an abstract interpretation technique to solve many of the flow analysis problems in a unified way to exploitation of parallelism and optimization of the code.
Chains of recurrences
The main contribution of this thesis are a precise and general formulation of the concepts and of theCR method, new algorithms for constructing, simplifying, and evaluating CR expressions, a numeric stability analysis of CR evaluations, and a stand-alone and flexible implementation of the CR method.
Symbolic analysis for parallelizing compilers
A methodology for capturing analyzing program properties that are essential in the effective detection and efficient exploitation of parallelism on parallel computers is described and a symbolic analysis framework is developed for the Parafrase-2 parallelizing compiler.
Beyond induction variables
A simple algorithm based on the Static Single Assignment form of a program that finds all linear induction variables in a loop and gives a unified approach to induction variable analysis, improves the speed of compilers and allows a more general classification scheme.
Recurrent Relations and Speed-up of Computations Using Computer Algebra Systems
A special algebraic method has been created that provides for the automatic construction of recurrent relations in the algorithms of cycle optimisation, in the computer algebra systems and in algorithms of automatic parallel programs construction.
Demand-Driven, Symbolic Range Propagation
This paper presents an algorithm that provides range analysis on-demand in parallelizing Fortran compilers, implemented in Polaris as well, and measured its effectiveness.
Chains of recurrences—a method to expedite the evaluation of closed-form functions
Chains of Recurrences are introduced as an effective method to evaluate functions at regular intervals and an implementation of the method in MAXIMA/Common Lisp is discussed.
Simplification and optimization transformations of chains of recurrences
  • E. Zima
  • Computer Science
    ISSAC '95
  • 1995
The Chain of Recurrences technique to expedite computations is extended by rational simplifications and examined as a form of internal representation, oriented towards fast evaluation.
Chains of recurrences for functions of two variables and their application to surface plotting
  • O. Bachmann
  • Mathematics
    Computer-Human Interaction in Symbolic Computation
  • 1998
When generating curves or surfaces of closed-form mathematical functions, usually the most time-consuming task is function evaluation at discrete points through whichever numerical evaluation routines the particular system provides.