Amdahl's Law

Amdahl's Law
Daniels220 at English Wikipedia · CC BY-SA 3.0 · source
Name	Amdahl's Law
Field	Computer science, Parallel computing
Introduced	1967
Named after	Gene Amdahl

Amdahl's Law Amdahl's Law is a principle in computer science and parallel computing that quantifies the potential speedup of a task using multiple processors, originally articulated by Gene Amdahl while at Amdahl Corporation and influencing designs at IBM, Intel, and Cray Research. The law highlights fundamental limits linked to the serial portion of workloads, informing research at institutions such as Massachusetts Institute of Technology, Stanford University, and University of California, Berkeley and shaping procurement decisions by organizations like NASA, European Space Agency, and Los Alamos National Laboratory. It appears in discussions alongside models like Gustafson's Law and in standards efforts at bodies such as the IEEE and ACM.

Overview and Definition

Amdahl's Law defines the maximum theoretical speedup in latency of executing a fixed-size problem using multiple processors, contrasting serial and parallel fractions in an application, a concept that informed designs at Bell Labs, Fairchild Semiconductor, and Hewlett-Packard. Gene Amdahl presented the idea in the context of mainframe performance debates involving IBM System/360, UNIVAC, and later supercomputer projects at Seymour Cray's firms, influencing curriculum at Carnegie Mellon University, Princeton University, and University of Illinois Urbana-Champaign. The law is often taught alongside models like Gustafson's Law and tools from the OpenMP and MPI communities.

Mathematical Formulation

Amdahl's original formulation expresses overall speedup S(P) as S(P) = 1 / ( (1 - f) + f / P ), where f is the fraction of execution time that is parallelizable and P is the number of processors, a relation used in analyses at Los Alamos National Laboratory, Sandia National Laboratories, and Argonne National Laboratory. This equation yields asymptotic limits as P → ∞ given by 1 / (1 - f), a bound referenced in papers from ACM SIGARCH, IEEE Transactions on Computers, and conferences such as SC (Supercomputing Conference). Variants incorporate overhead terms introduced by researchers at Bell Labs Research, MIT Lincoln Laboratory, and Intel Labs to model communication, synchronization, and contention.

Implications for Parallel Computing

Amdahl's Law implies diminishing returns when scaling processors for fixed workloads, influencing architecture choices at ARM Holdings, NVIDIA, AMD (company), and cloud providers like Amazon Web Services, Microsoft Azure, and Google Cloud Platform. It motivates emphasis on reducing serial bottlenecks in systems built by Oracle Corporation, Dell Technologies, and Hewlett Packard Enterprise and shapes compiler and runtime optimizations in projects at GNU Project, LLVM, and OpenMP Architecture Review Board. The law also underpins performance evaluation in benchmarking suites such as SPEC and in procurement policies at agencies like DARPA and European Commission research programs.

Extensions and Generalizations

Extensions include Gustafson's Law proposed by John L. Gustafson, which considers scaled problems and leads to different scalability conclusions used at NASA Ames Research Center and in workload studies by Lawrence Livermore National Laboratory. Generalizations introduce terms for communication latency, contention, and Amdahl-like efficiency factors developed by researchers at University of Cambridge, École Polytechnique Fédérale de Lausanne, and Technical University of Munich. Queueing-theory-based models by academics at Columbia University, University of Texas at Austin, and Yale University integrate Amdahl-style limits with service-time variability, while heterogeneity-aware models reference projects at Google Research and Facebook AI Research.

Practical Examples and Applications

Engineers apply Amdahl-style reasoning in optimizing software for multicore CPUs from Intel Corporation, Advanced Micro Devices, and accelerators from NVIDIA Corporation, and in tuning kernels for systems developed at Cray Inc. and Fujitsu. High-performance computing centers at Oak Ridge National Laboratory, Argonne National Laboratory, and NERSC use these principles when parallelizing simulation codes in domains like climate modeling at NOAA, computational chemistry at National Institutes of Health, and astrophysics at European Southern Observatory. Database vendors such as Oracle and PostgreSQL contributors, and big-data platforms from Apache Hadoop and Apache Spark communities, invoke Amdahl-like limits when designing distributed query engines and map-reduce pipelines.

Criticisms and Limitations

Critics note that Amdahl's Law applies to fixed-size problems and can underestimate achievable throughput when workloads scale, an argument central to Gustafson's critique and debated at conferences like Supercomputing and in journals from ACM and IEEE. It also abstracts away real-world factors—heterogeneous cores in ARM designs, network topologies from Infiniband vendors, and scheduling policies at cloud providers such as IBM Cloud—that affect scalability, as documented by researchers at MIT CSAIL, ETH Zurich, and University of Washington. Empirical studies from Sandia National Laboratories and industry benchmarking by SPEC reveal that synchronization, memory bandwidth, and I/O bottlenecks often dominate performance, limiting direct applicability of the idealized formula.

Category:Computer science