Chains of recurrences—a method to expedite the evaluation of closed-form functions

No abstract is available for this paper.

• Publication year

  1994

• Venue

  International Symposium on Symbolic and Algebraic Computation

• Publication date

  1994-08-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1145/190347.190423
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Recurrent Relations and Speed-up of Computations Using Computer Algebra Systems

  1992cited by this paper
• A System Independent Graphing Package for Mathematical Functions

  1990cited by this paper
• CRC standard mathematical tables

  1976influential reference

• Optimizing OpenCL Barrier Synchronization and Memory Efficiency on Multi-Core DSPs

  2025cites this paper
• Inductive Loop Analysis for Practical HPC Application Optimization

  2025cites this paper
• Systems Opportunities for LLM Fine-Tuning using Reinforcement Learning

  2025cites this paper
• Postiz: Extending Post-increment Addressing for Loop Optimization and Code Size Reduction

  2025cites this paper
• Dynamic Loop Fusion in High-Level Synthesis

  2025cites this paper
• Region-Based Data Layout via Data Reuse Analysis

  2024cites this paper
• LACT: Liveness-Aware Checkpointing to reduce checkpoint overheads in intermittent systems

  2024cites this paper
• Improving Memory Dependence Prediction with Static Analysis

  2024cites this paper
• Leveraging LLVM's ScalarEvolution for Symbolic Data Cache Analysis

  2023influential citation
• Liveness-Aware Checkpointing of Arrays for Efficient Intermittent Computing

  2023cites this paper
• Unifying Spatial Accelerator Compilation With Idiomatic and Modular Transformations

  2022cites this paper
• 20th International Workshop on Worst-Case Execution Time Analysis, WCET 2022, Modena, Italy, July 5, 2022

  2022cites this paper
• An architecture interface and offload model for low-overhead, near-data, distributed accelerators

  2022cites this paper
• A programmable, energy-minimal dataflow compiler and architecture

  2022cites this paper
• Piper: Pipelining OpenMP Offloading Execution Through Compiler Optimization For Performance

  2022cites this paper
• Combining Run-Time Checks and Compile-Time Analysis to Improve Control Flow Auto-Vectorization

  2022cites this paper
• LLVMTA: An LLVM-Based WCET Analysis Tool

  2022cites this paper
• Annotate once – analyze anywhere: context-aware WCET analysis by user-defined abstractions

  2021cites this paper
• PICO

  2021cites this paper
• OMPRacer: A Scalable and Precise Static Race Detector for OpenMP Programs

  2020cites this paper
• Autotuning for Automatic Parallelization on Heterogeneous Systems

  2020cites this paper
• Automated Finite State Machine Extraction

  2019cites this paper
• Precise reasoning with structured time, structured heaps, and collective operations

  2019cites this paper
• Automatic OpenCL Code Generation from LLVM-IR using Polyhedral Optimization

  2018cites this paper
• Loop-Oriented Pointer Analysis for Automatic SIMD Vectorization

  2018cites this paper
• VW-SLP: auto-vectorization with adaptive vector width

  2018cites this paper
• Look-ahead SLP: auto-vectorization in the presence of commutative operations

  2018cites this paper
• On one method of saving memory when classifying texts

  2017cites this paper
• Benchmark Generation for Timing Analysis

  2017cites this paper
• SuperGraph-SLP Auto-Vectorization

  2017cites this paper
• Borealis Bounded Model Checker: The Coming of Age Story

  2017cites this paper
• Optimistic loop optimization

  2017cites this paper
• An End-to-End Toolchain: From Automated Cost Modeling to Static WCET and WCEC Analysis

  2017cites this paper
• Eliminating Redundant Bounds Checks in Dynamic Buffer Overflow Detection Using Weakest Preconditions

  2016cites this paper
• ESTIMATIVA SIMBÓLICA DE INTERVALOS ASSUMIDOS POR VARIÁVEIS INTEIRAS DURANTE A EXECUÇÃO DE PROGRAMAS

  2016cites this paper
• Loop-oriented array- and field-sensitive pointer analysis for automatic SIMD vectorization

  2016influential citation
• Analysis and parameter prediction of compiler transformation for graphics processors

  2016cites this paper
• Throttling Automatic Vectorization: When Less is More

  2015cites this paper
• A Hybrid Approach for Parametric Memory Dependence Analysis

  2015cites this paper
• Worst-Case Energy Consumption Analysis for Energy-Constrained Embedded Systems

  2015cites this paper
• Accelerating Dynamic Detection of Memory Errors for C Programs via Static Analysis

  2015cites this paper
• WPBOUND: Enforcing Spatial Memory Safety Efficiently at Runtime with Weakest Preconditions

  2014cites this paper
• Feature-based device selection in heterogeneous computing systems

  2014cites this paper
• Accelerating Indefinite Summation: Simple Classes of Summands

  2013cites this paper
• A symbolic analysis framework for static analysis of imperative programming languages

  2012influential citation
• Polly – Polyhedral optimization in LLVM

  2012cites this paper
• Polly - Performing Polyhedral Optimizations on a Low-Level Intermediate Representation

  2012cites this paper
• Vérification partielle de programmes de contrôle-commande par interprétation abstraite

  2012cites this paper
• Interprocedural Static Single Assignment Form

  2011cites this paper
• Recursive symbolic bound analysis in loop structure

  2010cites this paper
• GCC for Parallelization

  2010cites this paper
• Verificarea acceselor la memorie în programe C folosind constrângeri simbolice s , i slicing

  2009cites this paper
• A unified compiler framework for program analysis, optimization, and automatic vectorization with chains of recurrences

  2009influential citation
• Automatic SIMD vectorization of chains of recurrences

  2008cites this paper
• Ada Asm GIMPLE − SSA GIMPLE Machine Description Induction variable analysis Data dependence analysis

  2008cites this paper
• Discovering Maximum Parallelization Using Advanced Data Dependence Analysis

  2008cites this paper
• Analyse statique par interprétation abstraite de systèmes hybrides

  2008cites this paper
• Proceedings of the GCC Developers' Summit

  2008cites this paper
• Methods for linear and nonlinear array data dependence analysis with the chains of recurrences algebra

  2007cites this paper
• E cient Symbolic Analysis forOptimizing Compilers ?

  2007influential citation
• Flow-Sensitive Loop-Variant Variable Classification in Linear Time

  2007cites this paper
• Model Manipulation as Part of a Better Development Process for Scientific Computing Code

  2007cites this paper
• The New Framework for Loop Nest Optimization in GCC: from Prototyping to Evaluation

  2006cites this paper
• The SSA Representation Framework: Semantics, Analyses and GCC Implementation

  2006cites this paper
• Symbolic Analysis of Imperative Programming Languages

  2006cites this paper
• SAFECode: A Platform for Developing Reliable Software in Unsafe Languages

  2006cites this paper
• COG-PETS: CODE GENERATION FOR PARAMETER ESTIMATION IN TIME SERIES

  2005cites this paper
• Memory safety without garbage collection for embedded applications

  2005cites this paper
• Induction Variable Analysis with Delayed Abstractions

  2005cites this paper
• Value Range Analysis of Conditionally Updated Variables and Pointers

  2004cites this paper
• A unified framework for nonlinear dependence testing and symbolic analysis

  2004cites this paper
• Array Data Dependence Testing with the Chains of Recurrences Algebra

  2004influential citation
• The CR# Algebra and its Application in Loop Analysis and Optimization

  2004cites this paper
• High-Level Loop Optimizations for GCC

  2004cites this paper
• Automatic validation of code-improving transformations on low-level program representations

  2004cites this paper
• Computational Divided Differencing and Divided-Difference Arithmetics

  2003influential citation
• Analysis of induction variables using chains of recurrences: exten-sions

  2003cites this paper
• Validation of code-improving transformations for embeded systems

  2003cites this paper
• 2 Horner ’ s Rule , embroidered , then improved

  2003cites this paper
• Code generation: evaluating polynomials

  2002cites this paper
• On computational properties of chains of recurrences

  2001cites this paper
• Efficient Symbolic Analysis for Optimizing Compilers

  2001cites this paper
• An efficient algorithm for pointer-to-array access conversion for compiling and optimizing DSP applications

  2001cites this paper
• Automatic Validation of Code-Improving Transformations

  2000cites this paper
• Symbolic Evaluation of Chains of Recurrencesfor Loop

  2000influential citation
• Code generation : evaluating polynomials

  2000cites this paper
• Traitement paresseux et optimisation des suites numriques

  2000cites this paper
• Lazy Processing and Optimization of Discrete Sequences

  1999cites this paper
• Chains of recurrences for functions of two variables and their application to surface plotting

  1998cites this paper
• Multidimensional chains of recurrences

  1998cites this paper
• Computer-Human Interaction in Symbolic Computation

  1998cites this paper
• Standalone MCR-based numerical engine

  1997cites this paper
• MPCR: an efficient and flexible chains of recurrences server

  1997cites this paper
• MPCR : An E cient and Flexible Chains

  1996cites this paper
• On Parallel Construction of Multidimensional Chains of Recurrences

  1996cites this paper
• Mapping techniques for parallel evaluation of chains of recurrences

  1996cites this paper
• MPCR: An E(cid:14)cient and Flexible Chains of Recurrences Server

  1996cites this paper
• On polynomial solutions of linear operator equations

  1995cites this paper
• Simplification and optimization transformations of chains of recurrences

  1995influential citation