Highly-reliable integer matrix multiplication via numerical packing

Anarado, Ijeoma; Anam, Mohammad Ashraful; Anastasia, Davide; Verdicchio, Fabio; Andreopoulos, Yiannis

doi:10.1109/iolts.2013.6604045

Cited by 3 publications

(5 citation statements)

References 10 publications

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“…previous work [40], our current proposal can operate both for SDC detection, as well as core failure mitigation. We focus on the latter in this paper, as it has already been deemed as a problem of high relevance to current cloud-computing deployments of multicore multimedia signal processing systems.…”

Section: B Contributionmentioning

confidence: 96%

“…Unlike our previous work on packing for detection of silent data corruptions (SDCs) in GEMM products [40], this paper focuses on core failure recovery in distributed systems assuming that the underlying parallel programming environment (like FT-MPI [41] and Open MPI [42]) detects such failures. However, if all output streams are received from all cores, our proposal can also be used for the detection of SDCs, since results can be cross-validated from outputs produced by execution in separate processing cores.…”

Section: B Contributionmentioning

confidence: 99%

“…The concept of numerical packing was originally proposed for throughput scaling in multimedia applications [20], [45], [48] and soft-error tolerance in GEMM for fail-continue systems (e.g., due to silent data corruption) [40]. Packed processing stacks multiple small dynamic-range inputs in a standard 32-bit or 64-bit representation using an integer packing factor, k, to avoid overflow (or "invasion"), and thereby performs computation on these inputs simultaneously.…”

Section: Brief Review Of Packing For Integer Data Computationsmentioning

confidence: 99%

“…The utilized value for k depends on the maximum possible value of the matrix product [20], [21], [45]. It has been shown that, to ensure accurate recovery of results after computation [20], [21], [40], [45], [49]:…”

Section: Brief Review Of Packing For Integer Data Computationsmentioning

confidence: 99%

“…with W ∈ {32, 64} if all processing is carried out in 32-bit or 64-bit integer representations and W ∈ {24, 52} if kernel processing is carried out in single or double-precision floatingpoint representations [20], [40].…”

Section: Brief Review Of Packing For Integer Data Computationsmentioning

confidence: 99%

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

Anarado

Andreopoulos

2016

IEEE Trans. Multimedia

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The decreasing meantime 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. In this paper, we propose a new roll-forward failure-mitigation approach for integer sum-of-product computations, with special emphasis on high-performance generic matrix multiplication (GEMM) and convolution/cross-correlation (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 from all 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 GEMM or CONV realizations performed on 32-bit integer representations. However, this bitwidth reduction is comparable to the one imposed due to the checksum elements of traditional roll-forward methods, especially for cases where multiple core failures must be mitigated. Experiments with state-of-the-art GEMM and CONV routines running on a c4.8xlarge (shared-memory, 18core) 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: (i) comparable to that of the conventional, failure-intolerant, integer GEMM and CONV routines; (ii) substantially superior to that of the equivalent rollforward 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: (i) 16%-23% cost reduction against the equivalent checksum-based method and (ii) more than 70% cost reduction against conventional failureintolerant processing based on AWS EC2 on-demand (i.e., highercost albeit guaranteed) instances.

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Section: B Contributionmentioning

confidence: 96%

Section: B Contributionmentioning

confidence: 99%

Section: Brief Review Of Packing For Integer Data Computationsmentioning

confidence: 99%

Section: Brief Review Of Packing For Integer Data Computationsmentioning

confidence: 99%

Section: Brief Review Of Packing For Integer Data Computationsmentioning

confidence: 99%

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

Anarado

Andreopoulos

2016

IEEE Trans. Multimedia

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Mitigation of fail-stop failures in integer matrix products via numerical packing

Anarado

Andreopoulos

2015

2015 IEEE 21st International on-Line Testing Symposium (IOLTS)

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

Anam

Andreopoulos

2016

IEEE Trans. Signal Process.

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Abstract-A new technique is proposed for fault-tolerant linear, sesquilinear and bijective (LSB) operations on M integer data streams (M ≥ 3), 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 several types of operations: 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 faultgenerating processor hardware or safety-critical applications, where high reliability is required without the cost of ABFT or modular redundancy.

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Highly-reliable integer matrix multiplication via numerical packing

Cited by 3 publications

References 10 publications

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

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

Mitigation of fail-stop failures in integer matrix products via numerical packing

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

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