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Energy-Efficient Iterative Refinement using Dynamic Precision

JunKyu Lee, Hans Vandierendonck, Mahwish Arif, Gregory D. Peterson, Dimitrios S. Nikolopoulos
2018 IEEE Journal on Emerging and Selected Topics in Circuits and Systems  
INTRODUCTION M IXED precision arithmetic is a promising approach to save energy when solving linear systems of equations in the form of Ax=b using iterative refinement.  ...  In this paper, utilising dynamic precisions and dynamic algorithm brings further speed-ups to conventional mixed precision iterative refinements without increasing the number of cores.  ...  APPENDIX A NUMERIC ANALYSIS FOR EACH STEP OF MIXED PRECISION ITERATIVE REFINEMENT In this section, we describe numeric analyses for a mixed precision iterative refinement of Algorithm I by utilising the  ... 
doi:10.1109/jetcas.2018.2850665 fatcat:r2ocwu62n5ehnomcfzjzzahl3a

The Design of Fast and Energy-Efficient Linear Solvers: On the Potential of Half-Precision Arithmetic and Iterative Refinement Techniques [chapter]

Azzam Haidar, Ahmad Abdelfattah, Mawussi Zounon, Panruo Wu, Srikara Pranesh, Stanimire Tomov, Jack Dongarra
2018 Lecture Notes in Computer Science  
The proposed energy-efficient linear system solvers are based on two main components: (1) iterative refinement techniques, and (2) reduced-precision computing features in modern accelerators and coprocessors  ...  By efficiently using the Tensor Cores available in the NVIDIA V100 PCIe GPUs, the speedups can be up to 4×, with more than 80% reduction in the energy consumption.  ...  Department of Energy Office of Science and the National Nuclear Security Administration. The work was also partially supported by NVIDIA and NSF grant No. OAC-1740250.  ... 
doi:10.1007/978-3-319-93698-7_45 fatcat:huozvhdhk5fqlhskmih4cpkyne

Energy Footprint of Advanced Dense Numerical Linear Algebra Using Tile Algorithms on Multicore Architectures

Jack Dongarra, Hatem Ltaief, Piotr Luszczek, Vincent M. Weaver
2012 2012 Second International Conference on Cloud and Green Computing  
We propose to study the impact on the energy footprint of two advanced algorithmic strategies in the context of high performance dense linear algebra libraries: (1) mixed precision algorithms with iterative  ...  refinement allow to run at the peak performance of single precision floating-point arithmetic while achieving double precision accuracy and (2) tree reduction technique exposes more parallelism when factorizing  ...  Furthermore, the use of mixed precision iterative refinement for sparse matrix problems [17] has lead to interesting conclusions in terms of energy efficiency and power consumption [18] , [19] .  ... 
doi:10.1109/cgc.2012.113 dblp:conf/cgc/DongarraLLW12 fatcat:6t2ghb3egffntmykfb4vr5t6um

Power Consumption of Mixed Precision in the Iterative Solution of Sparse Linear Systems

Hartwig Anzt, Vincent Heuveline, Bjorn Rocker, Maribel Castillo, Juan C. Fern´ndez, Rafael Mayo, Enrique S. Quintana-Orti
2011 2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum  
This paper presents a detailed analysis of a mixed precision iterative refinement solver applied to a linear system obtained from the 2D discretization of a fluid flow problem.  ...  The total execution time and energy need of different softand hardware-implementations are measured and compared with those of a plain GMRES-based solver in double precision.  ...  Fabregat, for their technical support with the energy measurement framework. The authors from the Universidad Jaume I were supported by project CICYT TIN2008-06570-C04-01 and FEDER.  ... 
doi:10.1109/ipdps.2011.226 dblp:conf/ipps/AnztHRCFMQ11 fatcat:z4ny7kpujzffnpgrrv3nmwvbvq

Studying Mixed Precision Techniques For The Solution Of Algebraic Riccati Equations

Peter Benner, Ernesto Dufrechou, Pablo Ezzatti, Alfredo Remón
2017 Zenodo  
The mixed-precision method obtains an approximation to the solution using single-precision arithmetic and then, this approximation is improved via a cheap iterative refinement.  ...  We evaluate different algorithms and the use of a mixed-precision approach for the solution of Algebraic Riccati Equations (AREs).  ...  For the mixed-precision scheme, we execute the proposal modifying the number of SDA and iterative refinement and steps.  ... 
doi:10.5281/zenodo.815496 fatcat:b7ia52rbcvayfj3azxdpsanu4a

On Dynamic Precision Scaling [article]

Serif Yesil, Ismail Akturk, Ulya R. Karpuzcu
2017 arXiv   pre-print
., accuracy loss) in computation during execution, this paper explores how Dynamic Precision Scaling (DPS) can maximize power efficiency by tailoring the precision of computation adaptively to temporal  ...  in accuracy due to precision reduction bounded.  ...  To handle these cases, DPS+ can be refined to track the actual call graphs of data dependent dynamic functions for precision matching.  ... 
arXiv:1709.06160v1 fatcat:vopba7arxfbsxh6ad3z7nb7bxe

Optimization of power consumption in the iterative solution of sparse linear systems on graphics processors

Hartwig Anzt, Maribel Castillo, Juan C. Fernández, Vincent Heuveline, Francisco D. Igual, Rafael Mayo, Enrique S. Quintana-Ortí
2011 Computer Science - Research and Development  
While the usage of iterative refinement combined with mixed precision arithmetic often improves the execution time of an iterative solver on a graphics processor, this may not necessarily be true for the  ...  To analyze the trade-off between computation time and power consumption we compare a plain GMRES solver and its preconditioned variant to the mixed-precision iterative refinement implementations based  ...  Roca, for their technical support with the energy measurement framework. The authors from the Universidad Jaume I were supported by project CICYT TIN2008-06570-C04-01 and FEDER.  ... 
doi:10.1007/s00450-011-0195-8 fatcat:po7yyo347nbihagg2hh77beeqi

Newly Elaborated Hybrid Algorithm for Optimization of Robot Arm's Trajectory in Order to Increase Efficiency and Provide Sustainability in Production

Rabab Benotsmane, László Dudás, György Kovács
2021 Sustainability  
This Hybrid Algorithm is based on the Tabu Search Algorithm and also uses two added methods—Point Insertion and Grid Refinement—simultaneously to find more precisely the optimal motion path of the robot  ...  The Hybrid Algorithm is executed using MATLAB software by creating a dynamic model of a 5 degree-of-freedom robot arm.  ...  Efficient and sustainable production means that the manufactured final products have to be competitive, cost-effective, energy-efficient and material-efficient, and produced by innovative, energy-saving  ... 
doi:10.3390/su13158193 fatcat:cevqpya4zvfmpiem2heozxcbci

E2-Train: Training State-of-the-art CNNs with Over 80 [article]

Yue Wang, Ziyu Jiang, Xiaohan Chen, Pengfei Xu, Yang Zhao, Yingyan Lin, Zhangyang Wang
2019 arXiv   pre-print
This paper attempts to explore an orthogonal direction: how to conduct more energy-efficient training of CNNs, so as to enable on-device training.  ...  model level; and sign prediction for low-cost, low-precision back-propagation, on the algorithm level.  ...  The authors would like to thank all anonymous reviewers for their tremendously useful comments to help improve our work.  ... 
arXiv:1910.13349v4 fatcat:pcoe2g42xfhfrh57swarlrlc7u

Truncated error correction for flexible approximate multiplication

Michael B. Sullivan, Earl E. Swartzlander
2012 2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR)  
Such approximate multipliers have been used in domain-specific applications, but existing designs either offer superior efficiency or flexibility.  ...  This study proposes a flexible approximate multiplier with improved efficiency.  ...  Non-iterative multipliers compute using a fixed precision which is set at design-time, providing superior efficiency but limited runtime flexibility.  ... 
doi:10.1109/acssc.2012.6489023 dblp:conf/acssc/SullivanS12 fatcat:e7wu7gygvvgkllm4bj3yembji4

Parallel adaptive solution for two dimensional 3-T energy equation on UG

Zeyao Mo
2006 Computing and Visualization in Science  
Two-dimensional (2D) energy equation coupled with three temperatures such as electron, ion and photon is widely used to approximately describe the evolution of radiation energy across multiple materials  ...  Significant numerical results using 32 processors are given and analyzed.  ...  Lang for using of framework UG. Thanks for the careful referee of paper reviewer.  ... 
doi:10.1007/s00791-006-0032-y fatcat:xhyop5hflna4rnrb6cbj4jojay

An Adaptive Contact Model for the Robust Simulation of Knots

Jonas Spillmann, Matthias Teschner
2008 Computer graphics forum (Print)  
Instead, their states are determined by employing a non-linear energy-minimization approach.  ...  Due to inherently complex contact configurations, the simulation of knot tying using rods is a challenging task.  ...  One rod is dynamically refined while the other rod has a fixed resolution. The four images illustrate that the dynamic behavior is not affected by the refinement.  ... 
doi:10.1111/j.1467-8659.2008.01147.x fatcat:qygih6abefdqjoddw2njsp2mnq

A Study of Sorting Algorithms on Approximate Memory

Shuang Chen, Shunning Jiang, Bingsheng He, Xueyan Tang
2016 Proceedings of the 2016 International Conference on Management of Data - SIGMOD '16  
It trades off precision for better performance and/or energy consumption.  ...  Our optimization gains the performance benefits by offloading the sorting operation to approximate storage, followed by an efficient refinement to resolve the unsortedness on the output of the approximate  ...  An approximate MLC configuration relaxes the strict precision constraints on iterative MLC writes to improve their performance and energy efficiency.  ... 
doi:10.1145/2882903.2882908 dblp:conf/sigmod/ChenJHT16 fatcat:li72pphkbrawtbxh6p2gj4dwhi

Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion

B. Philip, Z. Wang, M.A. Berrill, M. Birke, M. Pernice
2014 Journal of Computational Physics  
controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal  ...  To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multiphysics systems  ...  Red-black Gauss-Seidel is the smoother used on all refinement levels. All computations are performed in double precision on a Cray XK6 machine at ORNL.  ... 
doi:10.1016/j.jcp.2013.12.058 fatcat:de42xhr73vgdrmhleiomiyzraa

Mixed-precision in-memory computing

Manuel Le Gallo, Abu Sebastian, Roland Mathis, Matteo Manica, Heiner Giefers, Tomas Tuma, Costas Bekas, Alessandro Curioni, Evangelos Eleftheriou
2018 Nature Electronics  
The system therefore benefits from both the high precision of digital computing and the energy/areal efficiency of in-memory computing.  ...  Here we introduce the concept of mixed-precision in-memory computing, which combines a von Neumann machine with a computational memory unit.  ...  of digital computing and the energy/areal efficiency of in-memory computing.  ... 
doi:10.1038/s41928-018-0054-8 fatcat:3vah245ffneo7cuz44dzdmp4xi
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