Relevant bibliographies by topics / Mixed precision computation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Mixed precision computation'

Author: Grafiati
Published: 25 January 2025

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Journal articles on the topic "Mixed precision computation"

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Van Zee, Field G., Devangi N. Parikh, and Robert A. Van De Geijn. "Supporting Mixed-domain Mixed-precision Matrix Multiplication within the BLIS Framework." ACM Transactions on Mathematical Software 47, no. 2 (April 2021): 1–26. http://dx.doi.org/10.1145/3402225.

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We approach the problem of implementing mixed-datatype support within the general matrix multiplication ( gemm ) operation of the BLAS-like Library Instantiation Software framework, whereby each matrix operand A , B , and C may be stored as single- or double-precision real or complex values. Another factor of complexity, whereby the matrix product and accumulation are allowed to take place in a precision different from the storage precisions of either A or B , is also discussed. We first break the problem into orthogonal dimensions, considering the mixing of domains separately from mixing precisions. Support for all combinations of matrix operands stored in either the real or complex domain is mapped out by enumerating the cases and describing an implementation approach for each. Supporting all combinations of storage and computation precisions is handled by typecasting the matrices at key stages of the computation—during packing and/or accumulation, as needed. Several optional optimizations are also documented. Performance results gathered on a 56-core Marvell ThunderX2 and a 52-core Intel Xeon Platinum demonstrate that high performance is mostly preserved, with modest slowdowns incurred from unavoidable typecast instructions. The mixed-datatype implementation confirms that combinatorial intractability is avoided, with the framework relying on only two assembly microkernels to implement 128 datatype combinations.
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Al-Marakeby, A. "PRECISION ON DEMAND: A NOVEL LOSSLES MIXED-PRECISION COMPUTATION TECHNIQUE." Journal of Al-Azhar University Engineering Sector 15, no. 57 (October 1, 2020): 1046–56. http://dx.doi.org/10.21608/auej.2020.120378.

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Wang, Shengquan, Chao Wang, Yong Cai, and Guangyao Li. "A novel parallel finite element procedure for nonlinear dynamic problems using GPU and mixed-precision algorithm." Engineering Computations 37, no. 6 (February 22, 2020): 2193–211. http://dx.doi.org/10.1108/ec-07-2019-0328.

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Purpose The purpose of this paper is to improve the computational speed of solving nonlinear dynamics by using parallel methods and mixed-precision algorithm on graphic processing units (GPUs). The computational efficiency of traditional central processing units (CPUs)-based computer aided engineering software has been difficult to satisfy the needs of scientific research and practical engineering, especially for nonlinear dynamic problems. Besides, when calculations are performed on GPUs, double-precision operations are slower than single-precision operations. So this paper implemented mixed precision for nonlinear dynamic problem simulation using Belytschko-Tsay (BT) shell element on GPU. Design/methodology/approach To minimize data transfer between heterogeneous architectures, the parallel computation of the fully explicit finite element (FE) calculation is realized using a vectorized thread-level parallelism algorithm. An asynchronous data transmission strategy and a novel dependency relationship link-based method, for efficiently solving parallel explicit shell element equations, are used to improve the GPU utilization ratio. Finally, this paper implements mixed precision for nonlinear dynamic problems simulation using the BT shell element on a GPU and compare it to the CPU-based serially executed program and a GPU-based double-precision parallel computing program. Findings For a car body model containing approximately 5.3 million degrees of freedom, the computational speed is improved 25 times over CPU sequential computation, and approximately 10% over double-precision parallel computing method. The accuracy error of the mixed-precision computation is small and can satisfy the requirements of practical engineering problems. Originality/value This paper realized a novel FE parallel computing procedure for nonlinear dynamic problems using mixed-precision algorithm on CPU-GPU platform. Compared with the CPU serial program, the program implemented in this article obtains a 25 times acceleration ratio when calculating the model of 883,168 elements, which greatly improves the calculation speed for solving nonlinear dynamic problems.
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Liu, Xingchao, Mao Ye, Dengyong Zhou, and Qiang Liu. "Post-training Quantization with Multiple Points: Mixed Precision without Mixed Precision." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 10 (May 18, 2021): 8697–705. http://dx.doi.org/10.1609/aaai.v35i10.17054.

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We consider the post-training quantization problem, which discretizes the weights of pre-trained deep neural networks without re-training the model. We propose multipoint quantization, a quantization method that approximates a full-precision weight vector using a linear combination of multiple vectors of low-bit numbers; this is in contrast to typical quantization methods that approximate each weight using a single low precision number. Computationally, we construct the multipoint quantization with an efficient greedy selection procedure, and adaptively decides the number of low precision points on each quantized weight vector based on the error of its output. This allows us to achieve higher precision levels for important weights that greatly influence the outputs, yielding an ``effect of mixed precision'' but without physical mixed precision implementations (which requires specialized hardware accelerators). Empirically, our method can be implemented by common operands, bringing almost no memory and computation overhead. We show that our method outperforms a range of state-of-the-art methods on ImageNet classification and it can be generalized to more challenging tasks like PASCAL VOC object detection.
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Zhang, Jianfei, and Lei Zhang. "Efficient CUDA Polynomial Preconditioned Conjugate Gradient Solver for Finite Element Computation of Elasticity Problems." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/398438.

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Graphics processing unit (GPU) has obtained great success in scientific computations for its tremendous computational horsepower and very high memory bandwidth. This paper discusses the efficient way to implement polynomial preconditioned conjugate gradient solver for the finite element computation of elasticity on NVIDIA GPUs using compute unified device architecture (CUDA). Sliced block ELLPACK (SBELL) format is introduced to store sparse matrix arising from finite element discretization of elasticity with fewer padding zeros than traditional ELLPACK-based formats. Polynomial preconditioning methods have been investigated both in convergence and running time. From the overall performance, the least-squares (L-S) polynomial method is chosen as a preconditioner in PCG solver to finite element equations derived from elasticity for its best results on different example meshes. In the PCG solver, mixed precision algorithm is used not only to reduce the overall computational, storage requirements and bandwidth but to make full use of the capacity of the GPU devices. With SBELL format and mixed precision algorithm, the GPU-based L-S preconditioned CG can get a speedup of about 7–9 to CPU-implementation.
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Molina, Roméo, Vincent Lafage, David Chamont, and Fabienne Jézéquel. "Investigating mixed-precision for AGATA pulse-shape analysis." EPJ Web of Conferences 295 (2024): 03020. http://dx.doi.org/10.1051/epjconf/202429503020.

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The AGATA project aims at building a 4π gamma-ray spectrometer consisting of 180 germanium crystals, each crystal being divided into 36 segments. Each gamma ray produces an electrical signal within several neighbouring segments, which is compared with a data base of reference signals, enabling to locate the interaction. This step is called Pulse-Shape Analysis (PSA). In the execution chain leading to the PSA, we observe successive data conversions: the original 14-bit integers given by the electronics are finally converted to 32-bit floats. This made us wonder about the real numerical accuracy of the results, and investigate the use of shorter floats, with the hope to speedup the computation, and also reduce a major cache-miss problem. In this article, we first describe the numerical validation of the PSA code, thanks to the CADNA library. After the code being properly instrumented, CADNA performs each computation three times with a random rounding mode. This allows, for each operation, to evaluate the number of exact significant digits using a Student test with 95% confidence threshold. In a second step, we report our successes and challenges while refactoring the code so to mix different numerical formats, using high precision only when necessary, and taking benefit of hardware speedup elsewhere.
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Yang, Linjie, and Qing Jin. "FracBits: Mixed Precision Quantization via Fractional Bit-Widths." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 12 (May 18, 2021): 10612–20. http://dx.doi.org/10.1609/aaai.v35i12.17269.

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Model quantization helps to reduce model size and latency of deep neural networks. Mixed precision quantization is favorable with customized hardwares supporting arithmetic operations at multiple bit-widths to achieve maximum efficiency. We propose a novel learning-based algorithm to derive mixed precision models end-to-end under target computation constraints and model sizes. During the optimization, the bit-width of each layer / kernel in the model is at a fractional status of two consecutive bit-widths which can be adjusted gradually. With a differentiable regularization term, the resource constraints can be met during the quantization-aware training which results in an optimized mixed precision model. Our final models achieve comparable or better performance than previous quantization methods with mixed precision on MobilenetV1/V2, ResNet18 under different resource constraints on ImageNet dataset.
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Stupishin, Leonid U., and Konstantin E. Nikitin. "Mixed Finite Element of Geometrically Nonlinear Shallow Shells of Revolution." Applied Mechanics and Materials 501-504 (January 2014): 514–17. http://dx.doi.org/10.4028/www.scientific.net/amm.501-504.514.

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The computation method for shallow shell of revolution in mixed finite-element formulation is developed. Final equations are constructed by the Galerkin method. Results of solution of test task are represented. Precision and convergence of results is analyzed.
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Burkov, Andriy, and Brahim Chaib-draa. "An Approximate Subgame-Perfect Equilibrium Computation Technique for Repeated Games." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (July 4, 2010): 729–36. http://dx.doi.org/10.1609/aaai.v24i1.7623.

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This paper presents a technique for approximating, up to any precision, the set of subgame-perfect equilibria (SPE) in repeated games with discounting. The process starts with a single hypercube approximation of the set of SPE payoff profiles. Then the initial hypercube is gradually partitioned on to a set of smaller adjacent hypercubes, while those hypercubes that cannot contain any SPE point are gradually withdrawn. Whether a given hypercube can contain an equilibrium point is verified by an appropriate mixed integer program. A special attention is paid to the question of extracting players' strategies and their representability in form of finite automata.
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Lam, Michael O., and Jeffrey K. Hollingsworth. "Fine-grained floating-point precision analysis." International Journal of High Performance Computing Applications 32, no. 2 (June 15, 2016): 231–45. http://dx.doi.org/10.1177/1094342016652462.

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Floating-point computation is ubiquitous in high-performance scientific computing, but rounding error can compromise the results of extended calculations, especially at large scales. In this paper, we present new techniques that use binary instrumentation and modification to do fine-grained floating-point precision analysis, simulating any level of precision less than or equal to the precision of the original program. These techniques have an average of 40–70% lower overhead and provide more fine-grained insights into a program’s sensitivity than previous mixed-precision analyses. We also present a novel histogram-based visualization of a program’s floating-point precision sensitivity, as well as an incremental search technique that allows developers to incrementally trade off analysis time for detail, including the ability to restart analyses from where they left off. We present results from several case studies and experiments that show the efficacy of these techniques. Using our tool and its novel visualization, application developers can more quickly determine for specific data sets whether their application could be run using fewer double precision variables, saving both time and memory space.
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Dissertations / Theses on the topic "Mixed precision computation"

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Steffy, Daniel E. "Topics in exact precision mathematical programming." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39639.

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The focus of this dissertation is the advancement of theory and computation related to exact precision mathematical programming. Optimization software based on floating-point arithmetic can return suboptimal or incorrect resulting because of round-off errors or the use of numerical tolerances. Exact or correct results are necessary for some applications. Implementing software entirely in rational arithmetic can be prohibitively slow. A viable alternative is the use of hybrid methods that use fast numerical computation to obtain approximate results that are then verified or corrected with safe or exact computation. We study fast methods for sparse exact rational linear algebra, which arises as a bottleneck when solving linear programming problems exactly. Output sensitive methods for exact linear algebra are studied. Finally, a new method for computing valid linear programming bounds is introduced and proven effective as a subroutine for solving mixed-integer linear programming problems exactly. Extensive computational results are presented for each topic.
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Robeyns, Matthieu. "Mixed precision algorithms for low-rank matrix and tensor approximations." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASG095.

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La gestion des données est souvent réalisée par des objets mathématiques tels que les matrices et les tenseurs, qui sont la généralisation des matrices à plus de deux dimensions.Certains domaines d'application nécessitent de stocker trop d'éléments, créant des tenseurs trop grands ; ce problème est connu sous le nom de emph curse of dimensionality.Des méthodes mathématiques telles que les approximations de rang faible ont été développées pour réduire la dimensionnalité de ces objets malgré un coût très élevé en temps de calcul.De plus, de nouvelles architectures informatiques telles que les GPU nous permettent d'effectuer des calculs rapidement, notamment lors de calculs en faible précision.Combiner ces nouvelles architectures avec l'approximation de rang faible est une solution malgré la qualité des résultats altérée par la faible précision.Cette thèse vise à proposer des algorithmes d'approximation de rang faible stables en faible précision tout en conservant l'accélération inhérente au calcul en faible précision, ce qui est réalisable grâce au calcul en précision mixte.Nous avons développé une méthode générale d'approximation de tenseurs en précision mixte en calculant d'abord une approximation en faible précision et en l'affinant itérativement avec une précision supérieure pour maintenir la qualité du résultat.Sachant que cette accélération provient principalement des architectures GPU, plus précisément d'unités de calcul spécialisées appelées emph tensor cores, nous avons développé une méthode générale d'approximation matricielle pour les architectures GPU en précision mixte utilisant ces emph tensor cores.Notre méthode maintient la qualité du résultat, mais au prix d'une approximation de dimension supérieur à celle des applications standards.Pour compenser cet écart, des méthodes de recompression de dimension existent pour différents formats de tenseurs.Notre contribution finale propose une méthode de recompression englobant les différents formats de tenseurs et de matrices tout en prouvant analytiquement sa stabilité
Data management is often done by mathematical objects such as matrices and tensors, which are the generalization of matrices to more than two dimensions.Some application domains require too many elements to be stored, creating tensors too large; this problem is known as the emph curse of dimensionality.Mathematical methods such as low-rank approximations have been developed to reduce the dimensionality of these objects despite a very high cost in computation time.Moreover, new computer architectures such as GPUs allow us to perform computations quickly, especially when computing with low precision.Combining these new architectures with low-rank approximation is a solution despite the quality of the results being impaired by low precision.This thesis aims to propose low-rank approximation algorithms that are stable in low precision while maintaining the speedup inherent in low-precision computation, which is feasible thanks to mixed-precision computation.We have developed a general method for mixed-precision tensor approximation by first computing a low-precision approximation and iteratively refining it with higher precision to maintain the quality of the result.Knowing that this speedup comes mainly from GPU architectures, more precisely from specialized computing units called emph ensor cores, we have developed a general matrix approximation method for mixed-precision GPU architectures using these emph tensor cores.Our method maintains the quality of the result but at the expense of a higher-dimensional approximation than standard applications.To compensate for this gap, dimension recompression methods exist for different tensor formats.Our final contribution proposes a recompression method encompassing the different tensor and matrix formats while proving analytically its stability
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Books on the topic "Mixed precision computation"

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Li, Wei, Leilei Ji, Ramesh Agarwal, Weidong Shi, and Ling Zhou. Mixed-flow Pumps: Modeling, Simulation, and Measurements. ASME-Wiley, 2024. http://dx.doi.org/10.1115/1.862mfp.

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Learn to improve and optimize the design and operation of mixed-flow pumps. Mixed-flow pumps have a huge range of applications in agriculture, hydroelectric power, and other industries that incorporate fluid transport. They are centrifugal pumps incorporating the characteristics of both axial and radial pumps to increase the flow rate and discharge pressure. Though essential in a variety of industries, they pose serious challenges to numerical simulation methods, challenges which are starting to be met by the application of computational fluid dynamics using high-performance computing. Mixed-flow Pumps introduces engineers and researchers to this subject and its important applications. Incorporating all major varieties of mixed-flow pumps used in industrial applications, it employs methods from advanced computational fluid dynamics and high-precision flow field experimentation to characterize and analyze these crucial technologies. Moving from the fundamentals of the technology to its most advanced applications, it’s an essential resource for engineers and industry practitioners looking to develop their understanding of fluid transport. Mixed-flow Pumps readers will also find: Mixed-flow Pumps is a useful reference for mixed-flow pump design by academic researchers, including graduate students, industry practitioners, and test engineers.
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Book chapters on the topic "Mixed precision computation"

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Giraud, Luc, Azzam Haidar, and Layne T. Watson. "Mixed-Precision Preconditioners in Parallel Domain Decomposition Solvers." In Lecture Notes in Computational Science and Engineering, 357–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75199-1_44.

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Ben Khalifa, Dorra, Matthieu Martel, and Assalé Adjé. "POP: A Tuning Assistant for Mixed-Precision Floating-Point Computations." In Communications in Computer and Information Science, 77–94. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-46902-3_5.

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Carrillo, Carlos, Tomás Margalef, Antonio Espinosa, and Ana Cortés. "Impact of Mixed-Precision: A Way to Accelerate Data-Driven Forest Fire Spread Systems." In Computational Science – ICCS 2023, 62–76. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-36021-3_5.

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Glimberg, S. L., A. P. Engsig-Karup, and M. G. Madsen. "A Fast GPU-Accelerated Mixed-Precision Strategy for Fully Nonlinear Water Wave Computations." In Numerical Mathematics and Advanced Applications 2011, 645–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-33134-3_68.

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Halbiniak, Kamil, Krzysztof Rojek, Sergio Iserte, and Roman Wyrzykowski. "Unleashing the Potential of Mixed Precision in AI-Accelerated CFD Simulation on Intel CPU/GPU Architectures." In Computational Science – ICCS 2024, 203–17. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-63778-0_15.

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Freytag, Gabriel, João V. F. Lima, Paolo Rech, and Philippe O. A. Navaux. "Impact of Reduced and Mixed-Precision on the Efficiency of a Multi-GPU Platform on CFD Applications." In Computational Science and Its Applications – ICCSA 2022 Workshops, 570–87. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-10542-5_39.

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Baccar, Sahbi, Timothée Levi, Dominique Dallet, and François Barbara. "Optimizing Model Precision in High Temperatures for Efficient Analog and Mixed-Signal Circuit Design Using Modern Behavioral Modeling Technique: An Industrial Case Study." In Computational Intelligence in Analog and Mixed-Signal (AMS) and Radio-Frequency (RF) Circuit Design, 177–215. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19872-9_7.

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Goddeke, Dominik, and Robert Strzodka. "Mixed-Precision GPU-Multigrid Solvers with Strong Smoothers." In Chapman & Hall/CRC Computational Science, 131–47. CRC Press, 2010. http://dx.doi.org/10.1201/b10376-11.

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Barnett, R. N., P. J. Reynolds, and W. A. Lester. "Monte Carlo algorithms for expectation values of coordinate operators." In Quantum Monte Carlo, 77. Oxford University PressNew York, NY, 2007. http://dx.doi.org/10.1093/oso/9780195310108.003.0080.

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Abstract In diffusion QMC with importance sampling, walkers provide samples of configurations with probabilities proportional to the product of the true wave function ‘¢ and a trial wavefunction t/Jr. The expectation value of the energy (very fortunately) may be calculated from the local energies of these samples as E = (‘l/JH’l/Jr)/(‘l/Jt/Jr) = (‘l/JE10ct/Jr)/(‘¢’¢r). But for an operator A which does not commute with the Hamiltonian H, the mixed expectation value (‘¢At/Jr) is only an approximation to the “pure” expectation value (‘ljJA’¢). Thus, for most quantities of interest other than the energy, an extension to standard diffusion QMC methods is required. This paper describes two approaches to the problem. Both are based on an earlier development by Liu, Kalos, and Chester0 involving the tracking of descendents of walkers to obtain pure expectation values. The first uses simple DQMC and the second uses VQMC with DQMC “side walkers.” These methods were tested in their application to the model systems H and H2, and both were found effective in yielding accuracies and precisions correct within 0.5% for the quantities (r) for H and (r2) and (z2) for H and H2. The large differences in electron and proton masses led to extensive computation requirements due to the slow equilibration and serial correlation induced by the heavier protons. The calculations were executed on one of the first massively parallel computers, a Thinking Machines CM-2 with 65,536 processors. Frequent communication among the processors was required to balance the number of walkers treated in each.
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Conference papers on the topic "Mixed precision computation"

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Bertaccini, Luca, Siyuan Shen, Torsten Hoefler, and Luca Benini. "Extending RISC-V for Efficient Overflow Recovery in Mixed-Precision Computations." In 2024 IEEE 42nd International Conference on Computer Design (ICCD), 268–75. IEEE, 2024. https://doi.org/10.1109/iccd63220.2024.00048.

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Wang, Junjie, Zhi-Ming Li, Sheng Zuo, Shugang Jiang, and Xiaojie Dang. "A Mixed Precision Direct Electromagnetic Finite Element Solver on GPUs." In 2024 International Applied Computational Electromagnetics Society Symposium (ACES-China), 1–3. IEEE, 2024. http://dx.doi.org/10.1109/aces-china62474.2024.10699568.

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Gao, Bin. "Memristor Based Mixed-Precision Computation-in-Memory System." In 2023 International Conference on IC Design and Technology (ICICDT). IEEE, 2023. http://dx.doi.org/10.1109/icicdt59917.2023.10332328.

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Lam, Michael O., Jeffrey K. Hollingsworth, Bronis R. de Supinski, and Matthew P. Legendre. "Automatically adapting programs for mixed-precision floating-point computation." In the 27th international ACM conference. New York, New York, USA: ACM Press, 2013. http://dx.doi.org/10.1145/2464996.2465018.

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Ren, Xuanzhengbo, Masatoshi Kawai, Tetsuya Hoshino, Takahiro Katagiri, and Toru Nagai. "Auto-tuning Mixed-precision Computation by Specifying Multiple Regions." In 2023 Eleventh International Symposium on Computing and Networking (CANDAR). IEEE, 2023. http://dx.doi.org/10.1109/candar60563.2023.00031.

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Lam, Michael O., Bronis R. de Supinksi, Matthew P. LeGendre, and Jeffrey K. Hollingsworth. "Abstract: Automatically Adapting Programs for Mixed-Precision Floating-Point Computation." In 2012 SC Companion: High Performance Computing, Networking, Storage and Analysis (SCC). IEEE, 2012. http://dx.doi.org/10.1109/sc.companion.2012.231.

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Lam, Michael O., Bronis R. de Supinksi, Matthew P. LeGendre, and Jeffrey K. Hollingsworth. "Poster: Automatically Adapting Programs for Mixed-Precision Floating-Point Computation." In 2012 SC Companion: High Performance Computing, Networking, Storage and Analysis (SCC). IEEE, 2012. http://dx.doi.org/10.1109/sc.companion.2012.232.

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Miret, Santiago, Vui Seng Chua, Mattias Marder, Mariano Phiellip, Nilesh Jain, and Somdeb Majumdar. "Neuroevolution-enhanced multi-objective optimization for mixed-precision quantization." In GECCO '22: Genetic and Evolutionary Computation Conference. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3512290.3528692.

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Abdelfattah, Ahmad, Stanimire Tomov, and Jack Dongarra. "Towards Half-Precision Computation for Complex Matrices: A Case Study for Mixed Precision Solvers on GPUs." In 2019 IEEE/ACM 10th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA). IEEE, 2019. http://dx.doi.org/10.1109/scala49573.2019.00008.

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Tang, Ray. "Use Mixed Precision Data Types to Speed up Computation for Ultrasound Imaging Software." In 2022 7th International Conference on Intelligent Informatics and Biomedical Sciences (ICIIBMS). IEEE, 2022. http://dx.doi.org/10.1109/iciibms55689.2022.9971490.

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