Reliable Linear, Sesquilinear and Bijective Operations On Integer Data Streams Via Numerical Entanglement

A new technique is proposed for fault-tolerant linear, sesquilinear and bijective (LSB) operations on $M$ integer data streams ($M\geq3$), such as: scaling, additions/subtractions, inner or outer vector products, permutations and convolutions. In the proposed method, the $M$ input integer data streams are linearly superimposed to form $M$ numerically-entangled integer data streams that are stored in-place of the original inputs. A series of LSB operations can then be performed directly using these entangled data streams. The results are extracted from the $M$ entangled output streams by additions and arithmetic shifts. Any soft errors affecting any single disentangled output stream are guaranteed to be detectable via a specific post-computation reliability check. In addition, when utilizing a separate processor core for each of the $M$ streams, the proposed approach can recover all outputs after any single fail-stop failure. Importantly, unlike algorithm-based fault tolerance (ABFT) methods, the number of operations required for the entanglement, extraction and validation of the results is linearly related to the number of the inputs and does not depend on the complexity of the performed LSB operations. We have validated our proposal in an Intel processor (Haswell architecture with AVX2 support) via fast Fourier transforms, circular convolutions, and matrix multiplication operations. Our analysis and experiments reveal that the proposed approach incurs between $0.03\%$ to $7\%$ reduction in processing throughput for a wide variety of LSB operations. This overhead is 5 to 1000 times smaller than that of the equivalent ABFT method that uses a checksum stream. Thus, our proposal can be used in fault-generating processor hardware or safety-critical applications, where high reliability is required without the cost of ABFT or modular redundancy.Comment: to appear in IEEE Trans. on Signal Processing, 201

Core Failure Mitigation in Integer Sum-of-Product Computations on Cloud Computing Systems

The decreasing mean-time-to-failure estimates in cloud computing systems indicate that multimedia applications running on such environments should be able to mitigate an increasing number of core failures at runtime. We propose a new roll-forward failure-mitigation approach for integer sumof-product computations, with emphasis on generic matrix multiplication (GEMM)and convolution/crosscorrelation (CONV) routines. Our approach is based on the production of redundant results within the numerical representation of the outputs via the use of numerical packing.This differs fromall existing roll-forward solutions that require a separate set of checksum (or duplicate) results. Our proposal imposes 37.5% reduction in the maximum output bitwidth supported in comparison to integer sum-ofproduct realizations performed on 32-bit integer representations which is comparable to the bitwidth requirement of checksummethods for multiple core failure mitigation. Experiments with state-of-the-art GEMM and CONV routines running on a c4.8xlarge compute-optimized instance of amazon web services elastic compute cloud (AWS EC2) demonstrate that the proposed approach is able to mitigate up to one quadcore failure while achieving processing throughput that is: 1) comparable to that of the conventional, failure-intolerant, integer GEMM and CONV routines, 2) substantially superior to that of the equivalent roll-forward failure-mitigation method based on checksum streams. Furthermore, when used within an image retrieval framework deployed over a cluster of AWS EC2 spot (i.e., low-cost albeit terminatable) instances, our proposal leads to: 1) 16%-23% cost reduction against the equivalent checksum-based method and 2) more than 70% cost reduction against conventional failure-intolerant processing on AWS EC2 on-demand (i.e., highercost albeit guaranteed) instances

Reliable Linear, Sesquilinear, and Bijective Operations on Integer Data Streams Via Numerical Entanglement

A new technique is proposed for fault-tolerant linear, sesquilinear and bijective (LSB) operations on $M$ integer data streams ( $M \geq 3$), such as: scaling, additions/subtractions, inner or outer vector products, permutations and convolutions. In the proposed method, $M$ input integer data streams are linearly superimposed to form $M$ numerically-entangled integer data streams that are stored in-place of the original inputs. LSB operations can then be performed directly using these entangled data streams. The results are extracted from the $M$ entangled output streams by additions and arithmetic shifts. Any soft errors affecting one disentangled output stream are guaranteed to be detectable via a post-computation reliability check. Additionally, when utilizing a separate processor core for each stream, our approach can recover all outputs after any single fail-stop failure. Importantly, unlike algorithm-based fault tolerance (ABFT) methods, the number of operations required for the entire process is linearly related to the number of inputs and does not depend on the complexity of the performed LSB operations. We have validated our proposal in an Intel processor via several types of operations: fast Fourier transforms, convolutions, and matrix multiplication operations. Our analysis and experiments reveal that the proposed approach incurs between 0.03% to 7% reduction in processing throughput for numerous LSB operations. This overhead is 5 to 1000 times smaller than that of the equivalent ABFT method that uses a checksum stream. Thus, our proposal can be used in fault-generating processor hardware or safety-critical applications, where high reliability is required without the cost of ABFT or modular redundancy

Fault Tolerant Integer Data Computations: Algorithms and Applications

As computing units move to higher transistor integration densities and computing clusters become highly heterogeneous, studies begin to predict that, rather than being exceptions, data corruptions in memory and processor failures are likely to become more prevalent. It has therefore become imperative to improve the reliability of systems in the face of increasing soft error probabilities in memory and computing logic units of silicon CMOS integrated chips. This thesis introduces a new class of algorithms for fault tolerance in compute-intensive linear and sesquilinear (“one-and-half-linear”) data computations on integer data inputs within high-performance computing systems. The key difference between the proposed algorithms and existing fault tolerance methods is the elimination of the traditional requirement for additional hardware resources for system reliability. The first contribution of this thesis is in the detection of hardware-induced errors in integer matrix products. The proposed method of numerical packing for detecting a single error within a quadruple of matrix outputs is described in Chapter 2. The chapter includes analytic calculations of the proposed method’s computational complexity and reliability. Experimental results show that the proposed algorithm incurs comparable execution time overhead to existing algorithms for the detection and correction of a limited number of errors within generic matrix multiplication (GEMM) outputs. On the other hand, numerical packing becomes substantially more efficient in the mitigation of multiple errors. The achieved execution time gain of numerical packing is further analyzed with respect to its energy saving equivalent, thus paving the way for a new class of silent data corruption (SDC) mitigation method for integer matrix products that are fast, energy efficient, and highly reliable. A further advancement of the proposed numerical packing approach for the mitigation of core/processor failures in computing clusters (a.k.a., failstop failures) is described in Chapter 3 . The key advantage of this new packing approach is the ability to tolerate processor failures for all classes of sum-of-product computations. Because multimedia applications running on cloud computing platforms are now required to mitigate an increasing number of failures and outages at runtime, we analyze the efficiency of numerical packing within an image retrieval framework deployed over a cluster of AWS EC2 spot (i.e., low-cost albeit terminable) instances. Our results show that more than 70% reduction of cost can be achieved in comparison to conventional failure-intolerant processing based on AWS EC2 on-demand (i.e., higher-cost albeit guaranteed) instances. Finally, beyond numerical packing, we present a second approach for reliability in the case of linear and sesquilinear integer data computations by generalizing the recently-proposed concept of numerical entanglement. The proposed approach is capable of recovering from multiple fail-stop failures in a parallel/distributed computing environment. We present theoretical analysis of the computational and bit-width requirements of the proposed method in comparison to existing methods of checksum generation and processing. Our experiments with integer matrix products show that the proposed approach incurs 1.72% − 37.23% reduction in processing throughput in comparison to failure-intolerant processing while allowing for the mitigation of multiple fail-stop failures without the use of additional computing resources

Resiliency in numerical algorithm design for extreme scale simulations

This work is based on the seminar titled ‘Resiliency in Numerical Algorithm Design for Extreme Scale Simulations’ held March 1–6, 2020, at Schloss Dagstuhl, that was attended by all the authors. Advanced supercomputing is characterized by very high computation speeds at the cost of involving an enormous amount of resources and costs. A typical large-scale computation running for 48 h on a system consuming 20 MW, as predicted for exascale systems, would consume a million kWh, corresponding to about 100k Euro in energy cost for executing 1023 floating-point operations. It is clearly unacceptable to lose the whole computation if any of the several million parallel processes fails during the execution. Moreover, if a single operation suffers from a bit-flip error, should the whole computation be declared invalid? What about the notion of reproducibility itself: should this core paradigm of science be revised and refined for results that are obtained by large-scale simulation? Naive versions of conventional resilience techniques will not scale to the exascale regime: with a main memory footprint of tens of Petabytes, synchronously writing checkpoint data all the way to background storage at frequent intervals will create intolerable overheads in runtime and energy consumption. Forecasts show that the mean time between failures could be lower than the time to recover from such a checkpoint, so that large calculations at scale might not make any progress if robust alternatives are not investigated. More advanced resilience techniques must be devised. The key may lie in exploiting both advanced system features as well as specific application knowledge. Research will face two essential questions: (1) what are the reliability requirements for a particular computation and (2) how do we best design the algorithms and software to meet these requirements? While the analysis of use cases can help understand the particular reliability requirements, the construction of remedies is currently wide open. One avenue would be to refine and improve on system- or application-level checkpointing and rollback strategies in the case an error is detected. Developers might use fault notification interfaces and flexible runtime systems to respond to node failures in an application-dependent fashion. Novel numerical algorithms or more stochastic computational approaches may be required to meet accuracy requirements in the face of undetectable soft errors. These ideas constituted an essential topic of the seminar. The goal of this Dagstuhl Seminar was to bring together a diverse group of scientists with expertise in exascale computing to discuss novel ways to make applications resilient against detected and undetected faults. In particular, participants explored the role that algorithms and applications play in the holistic approach needed to tackle this challenge. This article gathers a broad range of perspectives on the role of algorithms, applications and systems in achieving resilience for extreme scale simulations. The ultimate goal is to spark novel ideas and encourage the development of concrete solutions for achieving such resilience holistically.Peer Reviewed"Article signat per 36 autors/es: Emmanuel Agullo, Mirco Altenbernd, Hartwig Anzt, Leonardo Bautista-Gomez, Tommaso Benacchio, Luca Bonaventura, Hans-Joachim Bungartz, Sanjay Chatterjee, Florina M. Ciorba, Nathan DeBardeleben, Daniel Drzisga, Sebastian Eibl, Christian Engelmann, Wilfried N. Gansterer, Luc Giraud, Dominik G ̈oddeke, Marco Heisig, Fabienne Jezequel, Nils Kohl, Xiaoye Sherry Li, Romain Lion, Miriam Mehl, Paul Mycek, Michael Obersteiner, Enrique S. Quintana-Ortiz, Francesco Rizzi, Ulrich Rude, Martin Schulz, Fred Fung, Robert Speck, Linda Stals, Keita Teranishi, Samuel Thibault, Dominik Thonnes, Andreas Wagner and Barbara Wohlmuth"Postprint (author's final draft

Acceptable Risk Criteria Catalogue for Technical Risk Management

Technical Risk Management plays a vital role for risks mitigation process. During the recent past, huge efforts have been made to perform Technical Risk Management during components development for different complex series products. Therefore a large database is available describing risk of failure scenarios combined with the estimations of technical as well as monetary impacts, time losses and risk probabilities for different major components of the complex machinery. The notion that there exists some level of risk acceptable to everyone is a difficult idea to reconcile and yet, without such a baseline, how can it ever be possible to set guideline values and standards, given that life can never be risk free? Therefore, there is a great need for a methodology, describing criteria for the risk acceptance. This thesis makes an attempt to contribute to the Technical Risk Management by answering the question, “What are acceptable risk criteria?” and provides a methodology for deriving an Acceptable Risk Criteria Catalogue (ARCC). This will help the decision makers to decide for an optimized mitigation budget in order to bring a product faster in the market