“QuanTaichi: a compiler for quantized simulations” by Hu, Liu, Yang, Xu, Kuang, et al. …

  • ©Yuanming Hu, Jiafeng Liu, Xuanda Yang, Mingkuan Xu, Ye Kuang, Weiwei Xu, Qiang Dai, William T. Freeman, and Frédo Durand




    QuanTaichi: a compiler for quantized simulations



    High-resolution simulations can deliver great visual quality, but they are often limited by available memory, especially on GPUs. We present a compiler for physical simulation that can achieve both high performance and significantly reduced memory costs, by enabling flexible and aggressive quantization. Low-precision (“quantized”) numerical data types are used and packed to represent simulation states, leading to reduced memory space and bandwidth consumption. Quantized simulation allows higher resolution simulation with less memory, which is especially attractive on GPUs. Implementing a quantized simulator that has high performance and packs the data tightly for aggressive storage reduction would be extremely labor-intensive and error-prone using a traditional programming language. To make the creation of quantized simulation practical, we have developed a new set of language abstractions and a compilation system. A suite of tailored domain-specific optimizations ensure quantized simulators often run as fast as the full-precision simulators, despite the overhead of encoding-decoding the packed quantized data types. Our programming language and compiler, based on Taichi, allow developers to effortlessly switch between different full-precision and quantized simulators, to explore the full design space of quantization schemes, and ultimately to achieve a good balance between space and precision. The creation of quantized simulation with our system has large benefits in terms of memory consumption and performance, on a variety of hardware, from mobile devices to workstations with high-end GPUs. We can simulate with levels of resolution that were previously only achievable on systems with much more memory, such as multiple GPUs. For example, on a single GPU, we can simulate a Game of Life with 20 billion cells (8× compression per pixel), an Eulerian fluid system with 421 million active voxels (1.6× compression per voxel), and a hybrid Eulerian-Lagrangian elastic object simulation with 235 million particles (1.7× compression per particle). At the same time, quantized simulations create physically plausible results. Our quantization techniques are complementary to existing acceleration approaches of physical simulation: they can be used in combination with these existing approaches, such as sparse data structures, for even higher scalability and performance.


    1. Mridul Aanjaneya, Ming Gao, Haixiang Liu, Christopher Batty, and Eftychios Sifakis. 2017. Power diagrams and sparse paged grids for high resolution adaptive liquids. ACM Transactions on Graphics (TOG) 36, 4 (2017), 1–12.Google ScholarDigital Library
    2. Ahmad Abdelfattah, Hartwig Anzt, Erik G Boman, Erin Carson, Terry Cojean, Jack Dongarra, Mark Gates, Thomas Grützmacher, Nicholas J Higham, Sherry Li, et al. 2020. A survey of numerical methods utilizing mixed precision arithmetic. arXiv preprint arXiv:2007.06674 (2020).Google Scholar
    3. Gilbert Louis Bernstein and Fredrik Kjolstad. 2016. Perspectives: Why New Programming Languages for Simulation? ACM Transactions on Graphics (TOG) 35, 2 (2016), 1–3.Google ScholarDigital Library
    4. Gilbert Louis Bernstein, Chinmayee Shah, Crystal Lemire, Zachary Devito, Matthew Fisher, Philip Levis, and Pat Hanrahan. 2016. Ebb: A DSL for physical simulation on CPUs and GPUs. ACM Trans. Graph. 35, 2 (2016), 21:1–21:12.Google ScholarDigital Library
    5. Stephen Chou, Fredrik Kjolstad, and Saman Amarasinghe. 2018. Format abstraction for sparse tensor algebra compilers. Proceedings of the ACM on Programming Languages 2, OOPSLA (2018), 1–30.Google ScholarDigital Library
    6. Matthieu Courbariaux, Itay Hubara, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. 2016. Binarized neural networks: Training deep neural networks with weights and activations constrained to+ 1 or-1. arXiv preprint arXiv:1602.02830 (2016).Google Scholar
    7. Zachary DeVito, Niels Joubert, Francisco Palacios, Stephen Oakley, Montserrat Medina, Mike Barrientos, Erich Elsen, Frank Ham, Alex Aiken, Karthik Duraisamy, et al. 2011. Liszt: A domain specific language for building portable mesh-based PDE solvers. In International Conference for High Performance Computing, Networking, Storage and Analysis. 9.Google ScholarDigital Library
    8. Christian Eisenacher, Gregory Nichols, Andrew Selle, and Brent Burley. 2013. Sorted deferred shading for production path tracing. In Computer Graphics Forum, Vol. 32. Wiley Online Library, 125–132.Google Scholar
    9. Ming Gao, Xinlei Wang, Kui Wu, Andre Pradhana-Tampubolon, Eftychios Sifakis, Yuksel Cem, and Chenfanfu Jiang. 2018. GPU Optimization of Material Point Methods. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 32, 4 (2018), 102.Google Scholar
    10. Yunhui Guo. 2018. A survey on methods and theories of quantized neural networks. arXiv preprint arXiv:1808.04752 (2018).Google Scholar
    11. Rama Karl Hoetzlein. 2016. GVDB: Raytracing sparse voxel database structures on the GPU. In Proceedings of High Performance Graphics. Eurographics Association, 109–117.Google Scholar
    12. Ben Houston, Michael B Nielsen, Christopher Batty, Ola Nilsson, and Ken Museth. 2006. Hierarchical RLE level set: A compact and versatile deformable surface representation. ACM Transactions on Graphics (TOG) 25, 1 (2006), 151–175.Google ScholarDigital Library
    13. Yuanming Hu. 2020. The Taichi programming language. In ACM SIGGRAPH 2020 Courses. 1–50.Google ScholarDigital Library
    14. Yuanming Hu, Luke Anderson, Tzu-Mao Li, Qi Sun, Nathan Carr, Jonathan Ragan-Kelley, and Frédo Durand. 2020. DiffTaichi: Differentiable Programming for Physical Simulation. ICLR (2020).Google Scholar
    15. Yuanming Hu, Yu Fang, Ziheng Ge, Ziyin Qu, Yixin Zhu, Andre Pradhana, and Chenfanfu Jiang. 2018. A moving least squares material point method with displacement discontinuity and two-way rigid body coupling. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 37, 4 (2018), 150.Google ScholarDigital Library
    16. Yuanming Hu, Tzu-Mao Li, Luke Anderson, Jonathan Ragan-Kelley, and Frédo Durand. 2019. Taichi: a language for high-performance computation on spatially sparse data structures. ACM Transactions on Graphics (TOG) 38, 6 (2019), 201.Google ScholarDigital Library
    17. Zhiao Huang, Yuanming Hu, Tao Du, Siyuan Zhou, Hao Su, Joshua B Tenenbaum, and Chuang Gan. 2021. PlasticineLab: A Soft-Body Manipulation Benchmark with Differentiable Physics. ICLR (2021).Google Scholar
    18. Itay Hubara, Matthieu Courbariaux, Daniel Soudry, Ran El-Yaniv, and Yoshua Bengio. 2017. Quantized neural networks: Training neural networks with low precision weights and activations. The Journal of Machine Learning Research 18, 1 (2017), 6869–6898.Google ScholarDigital Library
    19. IEEE. 2008. IEEE Standard for Floating-Point Arithmetic. IEEE Std 754-2008 (2008), 1–70. Google ScholarCross Ref
    20. Benoit Jacob, Skirmantas Kligys, Bo Chen, Menglong Zhu, Matthew Tang, Andrew Howard, Hartwig Adam, and Dmitry Kalenichenko. 2018. Quantization and training of neural networks for efficient integer-arithmetic-only inference. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 2704–2713.Google ScholarCross Ref
    21. Norman P Jouppi, Cliff Young, Nishant Patil, David Patterson, Gaurav Agrawal, Raminder Bajwa, Sarah Bates, Suresh Bhatia, Nan Boden, Al Borchers, et al. 2017b. In-datacenter performance analysis of a tensor processing unit. In Proceedings of the 44th annual international symposium on computer architecture. 1–12.Google ScholarDigital Library
    22. Norman P. Jouppi, Cliff Young, Nishant Patil, David Patterson, Gaurav Agrawal, Raminder Bajwa, Sarah Bates, Suresh Bhatia, Nan Boden, Al Borchers, Rick Boyle, Pierre-luc Cantin, Clifford Chao, Chris Clark, Jeremy Coriell, Mike Daley, Matt Dau, Jeffrey Dean, Ben Gelb, Tara Vazir Ghaemmaghami, Rajendra Gottipati, William Gulland, Robert Hagmann, C. Richard Ho, Doug Hogberg, John Hu, Robert Hundt, Dan Hurt, Julian Ibarz, Aaron Jaffey, Alek Jaworski, Alexander Kaplan, Harshit Khaitan, Daniel Killebrew, Andy Koch, Naveen Kumar, Steve Lacy, James Laudon, James Law, Diemthu Le, Chris Leary, Zhuyuan Liu, Kyle Lucke, Alan Lundin, Gordon MacKean, Adriana Maggiore, Maire Mahony, Kieran Miller, Rahul Nagarajan, Ravi Narayanaswami, Ray Ni, Kathy Nix, Thomas Norrie, Mark Omernick, Narayana Penukonda, Andy Phelps, Jonathan Ross, Matt Ross, Amir Salek, Emad Samadiani, Chris Severn, Gregory Sizikov, Matthew Snelham, Jed Souter, Dan Steinberg, Andy Swing, Mercedes Tan, Gregory Thorson, Bo Tian, Horia Toma, Erick Tuttle, Vijay Vasudevan, Richard Walter, Walter Wang, Eric Wilcox, and Doe Hyun Yoon. 2017a. In-Datacenter Performance Analysis of a Tensor Processing Unit. SIGARCH Comput. Archit. News 45, 2 (June 2017), 1–12. Google ScholarDigital Library
    23. Minje Kim and Paris Smaragdis. 2016. Bitwise neural networks. arXiv preprint arXiv:1601.06071 (2016).Google Scholar
    24. Fredrik Kjolstad, Shoaib Kamil, Stephen Chou, David Lugato, and Saman Amarasinghe. 2017. The tensor algebra compiler. Proceedings of the ACM on Programming Languages 1, OOPSLA (2017), 1–29.Google ScholarDigital Library
    25. Fredrik Kjolstad, Shoaib Kamil, Jonathan Ragan-Kelley, David I. W. Levin, Shinjiro Sueda, Desai Chen, Etienne Vouga, Danny M. Kaufman, Gurtej Kanwar, Wojciech Matusik, and Saman Amarasinghe. 2016. Simit: A language for physical simulation. ACM Trans. Graph. 35, 2 (2016), 20:1–20:21.Google ScholarDigital Library
    26. Haixiang Liu, Yuanming Hu, Bo Zhu, Wojciech Matusik, and Eftychios Sifakis. 2018. Narrow-band Topology Optimization on a Sparsely Populated Grid. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 37, 6 (2018), 251:1–251:14.Google Scholar
    27. Haixiang Liu, Nathan Mitchell, Mridul Aanjaneya, and Eftychios Sifakis. 2016. A scalable schur-complement fluids solver for heterogeneous compute platforms. ACM Transactions on Graphics (TOG) 35, 6 (2016), 1–12.Google ScholarDigital Library
    28. Aleka McAdams, Eftychios Sifakis, and Joseph Teran. 2010. A parallel multigrid Poisson solver for fluids simulation on large grids. In Symposium on Computer Animation. ACM/Eurographics Association, 65–74.Google Scholar
    29. Ken Museth. 2013. VDB: High-resolution sparse volumes with dynamic topology. ACM Trans. Graph. 32, 3 (2013), 27.Google ScholarDigital Library
    30. Jonathan Ragan-Kelley, Andrew Adams, Sylvain Paris, Marc Levoy, Saman Amarasinghe, and Frédo Durand. 2012. Decoupling algorithms from schedules for easy optimization of image processing pipelines. ACM Transactions on Graphics (TOG) 31, 4 (2012), 1–12.Google ScholarDigital Library
    31. Andrew Selle, Ronald Fedkiw, Byungmoon Kim, Yingjie Liu, and Jarek Rossignac. 2008. An unconditionally stable MacCormack method. Journal of Scientific Computing 35, 2-3 (2008), 350–371.Google ScholarDigital Library
    32. Rajsekhar Setaluri, Mridul Aanjaneya, Sean Bauer, and Eftychios Sifakis. 2014. SPGrid: A sparse paged grid structure applied to adaptive smoke simulation. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 33, 6 (2014), 205.Google ScholarDigital Library
    33. Alexey Stomakhin, Craig Schroeder, Lawrence Chai, Joseph Teran, and Andrew Selle. 2013. A material point method for snow simulation. ACM Transactions on Graphics (TOG) 32, 4 (2013), 102.Google ScholarDigital Library
    34. Andre Pradhana Tampubolon, Theodore Gast, Gergely Klár, Chuyuan Fu, Joseph Teran, Chenfanfu Jiang, and Ken Museth. 2017. Multi-species simulation of porous sand and water mixtures. ACM Transactions on Graphics (TOG) 36, 4 (2017), 1–11.Google ScholarDigital Library
    35. Xinlei Wang, Yuxing Qiu, Stuart R Slattery, Yu Fang, Minchen Li, Song-Chun Zhu, Yixin Zhu, Min Tang, Dinesh Manocha, and Chenfanfu Jiang. 2020. A massively parallel and scalable multi-cpu material point method. ACM Transactions on Graphics (TOG) 39, 4 (2020), 30–1.Google ScholarDigital Library
    36. Gregory J Ward. 1994. The RADIANCE lighting simulation and rendering system. In Proceedings of the 21st annual conference on Computer graphics and interactive techniques. 459–472.Google ScholarDigital Library
    37. Jun Wu, Christian Dick, and Rüdiger Westermann. 2015. A system for high-resolution topology optimization. IEEE transactions on visualization and computer graphics 22, 3 (2015), 1195–1208.Google Scholar
    38. Kui Wu, Nghia Truong, Cem Yuksel, and Rama Hoetzlein. 2018. Fast fluid simulations with sparse volumes on the GPU. In Computer Graphics Forum (Proc. Eurographics), Vol. 37. Wiley Online Library, 157–167.Google Scholar
    39. Jonas Zehnder, Rahul Narain, and Bernhard Thomaszewski. 2018. An advection-reflection solver for detail-preserving fluid simulation. ACM Transactions on Graphics (TOG) 37, 4 (2018), 1–8.Google ScholarDigital Library
    40. Jacob Ziv and Abraham Lempel. 1977. A universal algorithm for sequential data compression. IEEE Transactions on information theory 23, 3 (1977), 337–343.Google ScholarDigital Library

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