Convolutional neural networks (CNNs) are the core of most state-of-the-art deep learning algorithms specialized for object detection and classification. CNNs are both computationally complex and embarrassingly parallel. Two properties that leave room for potential software and hardware optimizations for embedded systems. Given a programmable hardware accelerator with a CNN oriented custom instructions set, the compiler's task is to exploit the hardware's full potential, while abiding with the hardware constraints and maintaining generality to run different CNN models with varying workload properties. Snowflake is an efficient and scalable hardware accelerator implemented on programmable logic devices. It implements a control pipeline for a custom instruction set. The goal of this paper is to present Snowflake's compiler that generates machine level instructions from Torch7 model description files. The main software design points explored in this work are: model structure parsing, CNN workload breakdown, loop rearrangement for memory bandwidth optimizations and memory access balancing. The performance achieved by compiler generated instructions matches against hand optimized code for convolution layers. Generated instructions also efficiently execute AlexNet and ResNet18 inference on Snowflake. Snowflake with @math processing units was synthesized on Xilinx's Zynq XC7Z045 FPGA. At @math MHz, AlexNet achieved in @math frames s and @math GB s of off-chip memory bandwidth, and @math frames s and @math GB s for ResNet18. Total on-chip power is @math W.
Memory transfer friendly computation tiling for CNN accelerators was explored in @cite_11 @cite_1 . In @cite_3 , block tiling with x-y axis ordering was used. They store tiles with extra overlap regions, called augmented-tiles, in DRAM to avoid multiple DMA transactions. This work also stores overlapped regions but it tiles at the granularity of row strips with channel major ordering to lower overlapped data replication. This lowers the required memory bandwidth.
@cite_1 @cite_3 @cite_11
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As convolution layers contribute most operations in convolutional neural network (CNN) algorithms, an effective convolution acceleration scheme significantly affects the efficiency and performance of a hardware CNN accelerator. Convolution in CNNs involves three-dimensional multiply and accumulate (MAC) operations with four levels of loops, which results in a large design space. Prior works either employ limited loop optimization techniques, e.g. loop unrolling, tiling and interchange, or only tune some of the design variables after the accelerator architecture and dataflow are already fixed. Without fully studying the convolution loop optimization before the hardware design phase, the resulting accelerator can hardly exploit the data reuse and manage data movement efficiently. This work overcomes these barriers by quantitatively analyzing and optimizing the design objectives (e.g. required memory access) of the CNN accelerator based on multiple design variables. We systematically explore the trade-offs of hardware cost by searching the design variable configurations, and propose a specific dataflow of hardware CNN acceleration to minimize the memory access and data movement while maximizing the resource utilization to achieve high performance. The proposed CNN acceleration scheme and architecture are demonstrated on a standalone Altera Arria 10 GX 1150 FPGA by implementing end-to-end VGG-16 CNN model and achieved 645.25 GOPS of throughput and 47.97 ms of latency, which is a >3.2× enhancement compared to state-of-the-art FPGA implementations of VGG model. Three-dimensional convolutional neural networks (3D CNNs) are used efficiently in many computer vision applications. Most previous work in this area has concentrated only on designing and optimizing accelerators for 2D CNN, with few attempts made to accelerate 3D CNN on FPGA. We find accelerating 3D CNNs on FPGA to be challenge due to their high computational complexity and storage demands. More importantly, although the computation patterns of 2D and 3D CNNs are analogous, the conventional approaches adopted for accelerating 2D CNNs may be unfit for 3D CNN acceleration. In this paper, in order to accelerate 2D and 3D CNNs using a uniform framework, we propose a uniform template-based architecture that uses templates based on the Winograd algorithm to ensure fast development of 2D and 3D CNN accelerators. Furthermore, we also develop a uniform analytical model to facilitate efficient design space explorations of 2D and 3D CNN accelerators based on our architecture. Finally, we demonstrate the effectiveness of the template-based architecture by implementing accelerators for real-life 2D and 3D CNNs (VGG16 and C3D) on multiple FPGA platforms. On S2C VUS440, we achieve up to 1.13 TOPS and 1.11 TOPS under low resource utilization for VGG16 and C3D, respectively. End-to-end comparisons with CPU and GPU solutions demonstrate that our implementation of C3D achieves gains of up to 13x and 60x in performance and energy relative to a CPU solution, and a 6.4x energy efficiency gain over a GPU solution. Emerging GPGPU architectures, along with programming models like CUDA and OpenCL, offer a cost-effective platform for many applications by providing high thread level parallelism at lower energy budgets. Unfortunately, for many general-purpose applications, available hardware resources of a GPGPU are not efficiently utilized, leading to lost opportunity in improving performance. A major cause of this is the inefficiency of current warp scheduling policies in tolerating long memory latencies. In this paper, we identify that the scheduling decisions made by such policies are agnostic to thread-block, or cooperative thread array (CTA), behavior, and as a result inefficient. We present a coordinated CTA-aware scheduling policy that utilizes four schemes to minimize the impact of long memory latencies. The first two schemes, CTA-aware two-level warp scheduling and locality aware warp scheduling, enhance per-core performance by effectively reducing cache contention and improving latency hiding capability. The third scheme, bank-level parallelism aware warp scheduling, improves overall GPGPU performance by enhancing DRAM bank-level parallelism. The fourth scheme employs opportunistic memory-side prefetching to further enhance performance by taking advantage of open DRAM rows. Evaluations on a 28-core GPGPU platform with highly memory-intensive applications indicate that our proposed mechanism can provide 33 average performance improvement compared to the commonly-employed round-robin warp scheduling policy. Convolutional Neural Network (CNN) is a powerful technique widely used in computer vision area, which also demands much more computations and memory resources than traditional solutions. The emerging met al-oxide resistive random-access memory (RRAM) and RRAM crossbar have shown great potential on neuromorphic applications with high energy efficiency. However, the interfaces between analog RRAM crossbars and digital peripheral functions, namely Analog-to-Digital Converters (AD-Cs) and Digital-to-Analog Converters (DACs), consume most of the area and energy of RRAM-based CNN design due to the large amount of intermediate data in CNN. In this paper, we propose an energy efficient structure for RRAM-based CNN. Based on the analysis of data distribution, a quantization method is proposed to transfer the intermediate data into 1 bit and eliminate DACs. An energy efficient structure using input data as selection signals is proposed to reduce the ADC cost for merging results of multiple crossbars. The experimental results show that the proposed method and structure can save 80 area and more than 95 energy while maintaining the same or comparable classification accuracy of CNN on MNIST. In recent years, convolutional neural networks (CNNs) based machine learning algorithms have been widely applied in computer vision applications. However, for large-scale CNNs, the computation-intensive, memory-intensive and resource-consuming features have brought many challenges to CNN implementations. This work proposes an end-to-end FPGA-based CNN accelerator with all the layers mapped on one chip so that different layers can work concurrently in a pipelined structure to increase the throughput. A methodology which can find the optimized parallelism strategy for each layer is proposed to achieve high throughput and high resource utilization. In addition, a batch-based computing method is implemented and applied on fully connected layers (FC layers) to increase the memory bandwidth utilization due to the memory-intensive feature. Further, by applying two different computing patterns on FC layers, the required on-chip buffers can be reduced significantly. As a case study, a state-of-the-art large-scale CNN, AlexNet, is implemented on Xilinx VC709. It can achieve a peak performance of 565.94 GOP s and 391 FPS under 156MHz clock frequency which outperforms previous approaches. In the near future, cameras will be used everywhere as flexible sensors for numerous applications. For mobility and privacy reasons, the required image processing should be local on embedded computer platforms with performance requirements and energy constraints. Dedicated acceleration of Convolutional Neural Networks (CNN) can achieve these targets with enough flexibility to perform multiple vision tasks. A challenging problem for the design of efficient accelerators is the limited amount of external memory bandwidth. We show that the effects of the memory bottleneck can be reduced by a flexible memory hierarchy that supports the complex data access patterns in CNN workload. The efficiency of the on-chip memories is maximized by our scheduler that uses tiling to optimize for data locality. Our design flow ensures that on-chip memory size is minimized, which reduces area and energy usage. The design flow is evaluated by a High Level Synthesis implementation on a Virtex 6 FPGA board. Compared to accelerators with standard scratchpad memories the FPGA resources can be reduced up to 13× while maintaining the same performance. Alternatively, when the same amount of FPGA resources is used our accelerators are up to 11× faster. SIMD organizations amortize the area and power of fetch, decode, and issue logic across multiple processing units in order to maximize throughput for a given area and power budget. However, throughput is reduced when a set of threads operating in lockstep (a warp) are stalled due to long latency memory accesses. The resulting idle cycles are extremely costly. Multi-threading can hide latencies by interleaving the execution of multiple warps, but deep multi-threading using many warps dramatically increases the cost of the register files (multi-threading depth x SIMD width), and cache contention can make performance worse. Instead, intra-warp latency hiding should first be exploited. This allows threads that are ready but stalled by SIMD restrictions to use these idle cycles and reduces the need for multi-threading among warps. This paper introduces dynamic warp subdivision (DWS), which allows a single warp to occupy more than one slot in the scheduler without requiring extra register file space. Independent scheduling entities allow divergent branch paths to interleave their execution, and allow threads that hit to run ahead. The result is improved latency hiding and memory level parallelism (MLP). We evaluate the technique on a coherent cache hierarchy with private L1 caches and a shared L2 cache. With an area overhead of less than 1 , experiments with eight data-parallel benchmarks show our technique improves performance on average by 1.7X. Convolutional neural network (CNN) has been widely employed for image recognition because it can achieve high accuracy by emulating behavior of optic nerves in living creatures. Recently, rapid growth of modern applications based on deep learning algorithms has further improved research and implementations. Especially, various accelerators for deep CNN have been proposed based on FPGA platform because it has advantages of high performance, reconfigurability, and fast development round, etc. Although current FPGA accelerators have demonstrated better performance over generic processors, the accelerator design space has not been well exploited. One critical problem is that the computation throughput may not well match the memory bandwidth provided an FPGA platform. Consequently, existing approaches cannot achieve best performance due to under-utilization of either logic resource or memory bandwidth. At the same time, the increasing complexity and scalability of deep learning applications aggravate this problem. In order to overcome this problem, we propose an analytical design scheme using the roofline model. For any solution of a CNN design, we quantitatively analyze its computing throughput and required memory bandwidth using various optimization techniques, such as loop tiling and transformation. Then, with the help of rooine model, we can identify the solution with best performance and lowest FPGA resource requirement. As a case study, we implement a CNN accelerator on a VC707 FPGA board and compare it to previous approaches. Our implementation achieves a peak performance of 61.62 GFLOPS under 100MHz working frequency, which outperform previous approaches significantly. Eyeriss is an accelerator for state-of-the-art deep convolutional neural networks (CNNs). It optimizes for the energy efficiency of the entire system, including the accelerator chip and off-chip DRAM, for various CNN shapes by reconfiguring the architecture. CNNs are widely used in modern AI systems but also bring challenges on throughput and energy efficiency to the underlying hardware. This is because its computation requires a large amount of data, creating significant data movement from on-chip and off-chip that is more energy-consuming than computation. Minimizing data movement energy cost for any CNN shape, therefore, is the key to high throughput and energy efficiency. Eyeriss achieves these goals by using a proposed processing dataflow, called row stationary (RS), on a spatial architecture with 168 processing elements. RS dataflow reconfigures the computation mapping of a given shape, which optimizes energy efficiency by maximally reusing data locally to reduce expensive data movement, such as DRAM accesses. Compression and data gating are also applied to further improve energy efficiency. Eyeriss processes the convolutional layers at 35 frames s and 0.0029 DRAM access multiply and accumulation (MAC) for AlexNet at 278 mW (batch size @math ), and 0.7 frames s and 0.0035 DRAM access MAC for VGG-16 at 236 mW ( @math ). In this paper, we present techniques that coordinate the thread scheduling and prefetching decisions in a General Purpose Graphics Processing Unit (GPGPU) architecture to better tolerate long memory latencies. We demonstrate that existing warp scheduling policies in GPGPU architectures are unable to effectively incorporate data prefetching. The main reason is that they schedule consecutive warps, which are likely to access nearby cache blocks and thus prefetch accurately for one another, back-to-back in consecutive cycles. This either 1) causes prefetches to be generated by a warp too close to the time their corresponding addresses are actually demanded by another warp, or 2) requires sophisticated prefetcher designs to correctly predict the addresses required by a future "far-ahead" warp while executing the current warp. We propose a new prefetch-aware warp scheduling policy that overcomes these problems. The key idea is to separate in time the scheduling of consecutive warps such that they are not executed back-to-back. We show that this policy not only enables a simple prefetcher to be effective in tolerating memory latencies but also improves memory bank parallelism, even when prefetching is not employed. Experimental evaluations across a diverse set of applications on a 30-core simulated GPGPU platform demonstrate that the prefetch-aware warp scheduler provides 25 and 7 average performance improvement over baselines that employ prefetching in conjunction with, respectively, the commonly-employed round-robin scheduler or the recently-proposed two-level warp scheduler. Moreover, when prefetching is not employed, the prefetch-aware warp scheduler provides higher performance than both of these baseline schedulers as it better exploits memory bank parallelism. Hardware data prefetching is widely adopted to hide long memory latency. A hardware data prefetcher predicts the memory address that will be accessed in the near future and fetches the data at the predicted address into the cache memory in advance. To detect memory access patterns such as a constant stride, most existing prefetchers use differences between addresses in a sequence of memory accesses. However, prefetching based on the differences often fail to detect memory access patterns when aggressive optimizations are applied. For example, out-of-order execution changes the memory access order. It causes inaccurate prediction because the sequence of memory addresses used to calculate the difference are changed by the optimization. To overcome the problems of existing prefetchers, we propose Access Map Pattern Matching (AMPM). The AMPM prefetcher has two key components: a memory access map and hardware pattern matching logic. The memory access map is a bitmap-like data structure for holding past memory accesses. The AMPM prefetcher divides the memory address space into memory regions of a fixed size. The memory access map is mapped to the memory region. Each entry in the bitmap-like data structure is mapped to each cache line in the region. Once the bitmap is mapped to the memory region, the entry records whether the corresponding line has already been accessed or not. The AMPM prefetcher detects memory access patterns from the bitmap-like data structure that is mapped to the accessed region. The hardware pattern matching logic is used to detect stride access patterns in the memory access map. The result of pattern matching is affected by neither the memory access order nor the instruction addresses because the bitmap-like data structure holds neither the information that reveals the memory access order of past memory accesses nor the instruction addresses. Therefore, the AMPM prefetcher achieves high performance even when such aggressive optimizations are applied. The AMPM prefetcher is evaluated by performing cycle-accurate simulations using the memory-intensive benchmarks in the SPEC CPU2006 and the NAS Parallel Benchmark. In an aggressively optimized environment, the AMPM prefetcher improves prefetch coverage, while the other state-of-the-art prefetcher degrades the prefetch coverage significantly. As a result, the AMPM prefetcher increases IPC by 32.4 compared to state-of-the-art prefetcher. FPGA-based CNN accelerators have advantages in flexibility and power efficiency and so are being deployed by a number of cloud computing service providers, including Microsoft, Amazon, Tencent, and Alibaba. Given the increasing complexity of neural networks, however, it is becoming challenging to efficiently map CNNs to multi-FPGA platforms. In this work, we present a scalable framework, FPDeep, which helps engineers map a specific CNN's training logic to a multi-FPGA cluster or cloud and to build RTL implementations for the target network. With FPDeep, multi-FPGA accelerators work in a deeply-pipelined manner using a simple 1-D topology; this enables the accelerators to map directly onto many existing platforms, including Catapult, Catapult2, and almost any tightly-coupled FPGA cluster. FPDeep uses two mechanisms to facilitate high-performance and energy-efficiency. First, FPDeep provides a strategy to balance workload among FPGAs, leading to improved utilization. Second, training of CNNs is executed in a fine-grained inter- and intra-layer pipelined manner, minimizing the time that features need to remain available while waiting for back-propagation. This reduces the storage demand to where only on-chip memory is required for convolution layers. Experiments show that FPDeep has good scalability to a large number of FPGAs, with the limiting factor being the FPGA-to-FPGA bandwidth. Using six transceivers per FPGA, FPDeep shows linearity up to 60 FPGAs. We evaluate energy efficiency in GOPs J and find that FPDeep provides up to 3.4 times higher energy efficiency than the Tesla K80 GPU. This paper proposes tiling techniques based on data dependencies and not in code structure. The work presented here leverages and expands previous work by the authors in the domain of non traditional tiling for parallel applications. The main contributions of this paper are: (1) A formal description of tiling from the point of view of the data produced and not from the source code. (2) A mathematical proof for an optimum tiling in terms of maximum reuse for stencil applications, addressing the disparity between computation power and memory bandwidth for many-core architectures. (3) A description and implementation of our tiling technique for well known stencil applications. (4) Experimental evidence that confirms the effectiveness of the tiling proposed to alleviate the disparity between computation power and memory bandwidth for many-core architectures. Our experiments, performed using one of the first Cyclops-64 many-core chips produced, confirm the effectiveness of our approach to reduce the total number of memory operations of stencil applications as well as the running time of the application. Globally modeling and reasoning over relations between regions can be beneficial for many computer vision tasks on both images and videos. Convolutional Neural Networks (CNNs) excel at modeling local relations by convolution operations, but they are typically inefficient at capturing global relations between distant regions and require stacking multiple convolution layers. In this work, we propose a new approach for reasoning globally in which a set of features are globally aggregated over the coordinate space and then projected to an interaction space where relational reasoning can be efficiently computed. After reasoning, relation-aware features are distributed back to the original coordinate space for down-stream tasks. We further present a highly efficient instantiation of the proposed approach and introduce the Global Reasoning unit (GloRe unit) that implements the coordinate-interaction space mapping by weighted global pooling and weighted broadcasting, and the relation reasoning via graph convolution on a small graph in interaction space. The proposed GloRe unit is lightweight, end-to-end trainable and can be easily plugged into existing CNNs for a wide range of tasks. Extensive experiments show our GloRe unit can consistently boost the performance of state-of-the-art backbone architectures, including ResNet, ResNeXt, SE-Net and DPN, for both 2D and 3D CNNs, on image classification, semantic segmentation and video action recognition task. In commercial-off-the-shelf (COTS) multi-core systems, the execution times of tasks become hard to predict because of contention on shared resources in the memory hierarchy. In particular, a task running in one processor core can delay the execution of another task running in another processor core. This is due to the fact that tasks can access data in the same cache set shared among processor cores or in the same memory bank in the DRAM memory (or both). Such cache and bank interference effects have motivated the need to create isolation mechanisms for resources accessed by more than one task. One popular isolation mechanism is cache coloring that divides the cache into multiple partitions. With cache coloring, each task can be assigned exclusive cache partitions, thereby preventing cache interference from other tasks. Similarly, bank coloring allows assigning exclusive bank partitions to tasks. While cache coloring and some bank coloring mechanisms have been studied separately, interactions between the two schemes have not been studied. Specifically, while memory accesses to two different bank colors do not interfere with each other at the bank level, they may interact at the cache level. Similarly, two different cache colors avoid cache interference but may not prevent bank interference. Therefore it is necessary to coordinate cache and bank coloring approaches. In this paper, we present a coordinated cache and bank coloring scheme that is designed to prevent cache and bank interference simultaneously. We also developed color allocation algorithms for configuring a virtual memory system to support our scheme which has been implemented in the Linux kernel. In our experiments, we observed that the execution time can increase by 60 due to inter-task interference when we use only cache coloring. Our coordinated approach can reduce this figure down to 12 (an 80 reduction). Convolutional Neural Networks (CNNs) have gained popularity in many computer vision applications such as image classification, face detection, and video analysis, because of their ability to train and classify with high accuracy. Due to multiple convolution and fully-connected layers that are compute- memory-intensive, it is difficult to perform real-time classification with low power consumption on today?s computing systems. FPGAs have been widely explored as hardware accelerators for CNNs because of their reconfigurability and energy efficiency, as well as fast turn-around-time, especially with high-level synthesis methodologies. Previous FPGA-based CNN accelerators, however, typically implemented generic accelerators agnostic to the CNN configuration, where the reconfigurable capabilities of FPGAs are not fully leveraged to maximize the overall system throughput. In this work, we present a systematic design space exploration methodology to maximize the throughput of an OpenCL-based FPGA accelerator for a given CNN model, considering the FPGA resource constraints such as on-chip memory, registers, computational resources and external memory bandwidth. The proposed methodology is demonstrated by optimizing two representative large-scale CNNs, AlexNet and VGG, on two Altera Stratix-V FPGA platforms, DE5-Net and P395-D8 boards, which have different hardware resources. We achieve a peak performance of 136.5 GOPS for convolution operation, and 117.8 GOPS for the entire VGG network that performs ImageNet classification on P395-D8 board. The objective of this paper is to extend, in the context of multicore architectures, the concepts of tile algorithms [, 2007] for Cholesky, LU, and QR factorizations to the family of two-sided factorizations. In particular, the bidiagonal reduction of a general, dense matrix is very often used as a preprocessing step for calculating the Singular Value Decomposition. Furthermore, in the Top500 list of June 2008, 98 percent of the fastest parallel systems in the world were based on multicores. This confronts the scientific software community with both a daunting challenge and a unique opportunity. The challenge arises from the disturbing mismatch between the design of systems based on this new chip architecture-hundreds of thousands of nodes, a million or more cores, reduced bandwidth and memory available to cores-and the components of the traditional software stack, such as numerical libraries, on which scientific applications have relied for their accuracy and performance. The many-core trend has even more exacerbated the problem, and it becomes critical to efficiently integrate existing or new numerical linear algebra algorithms suitable for such hardware. By exploiting the concept of tile algorithms in the multicore environment (i.e., high level of parallelism with fine granularity and high-performance data representation combined with a dynamic data-driven execution), the band bidiagonal reduction presented here achieves 94 Gflop s on a 12,000 × 12,000 matrix with 16 Intel Tigerton 2.4 GHz processors. The main drawback of the tile algorithms approach for the bidiagonal reduction is that the full reduction cannot be obtained in one stage. Other methods have to be considered to further reduce the band matrix to the required form. Convolutional neural network (CNN) has become a successful algorithm in the region of artificial intelligence and a strong candidate for many computer vision algorithms. But the computation complexity of CNN is much higher than traditional algorithms. With the help of GPU acceleration, CNN-based applications are widely deployed in servers. However, for embedded platforms, CNN-based solutions are still too complex to be applied. Various dedicated hardware designs on field-programmable gate arrays (FPGAs) have been carried out to accelerate CNNs, while few of them explore the whole design flow for both fast deployment and high power efficiency. In this paper, we investigate state-of-the-art CNN models and CNN-based applications. Requirements on memory, computation and the flexibility of the system are summarized for mapping CNN on embedded FPGAs. Based on these requirements, we propose Angel-Eye, a programmable and flexible CNN accelerator architecture, together with data quantization strategy and compilation tool. Data quantization strategy helps reduce the bit-width down to 8-bit with negligible accuracy loss. The compilation tool maps a certain CNN model efficiently onto hardware. Evaluated on Zynq XC7Z045 platform, Angel-Eye is @math faster and @math better in power efficiency than peer FPGA implementation on the same platform. Applications of VGG network, pedestrian detection and face alignment are used to evaluate our design on Zynq XC7Z020. NIVIDA TK1 and TX1 platforms are used for comparison. Angel-Eye achieves similar performance and delivers up to @math better energy efficiency. Manycore accelerators such as graphics processor units (GPUs) organize processing units into single-instruction, multiple data “cores” to improve throughput per unit hardware cost. Programming models for these accelerators encourage applications to run kernels with large groups of parallel scalar threads. The hardware groups these threads into warps wavefronts and executes them in lockstep-dubbed single-instruction, multiple-thread (SIMT) by NVIDIA. While current GPUs employ a per-warp (or per-wavefront) stack to manage divergent control flow, it incurs decreased efficiency for applications with nested, data-dependent control flow. In this paper, we propose and evaluate the benefits of extending the sharing of resources in a block of warps, already used for scratchpad memory, to exploit control flow locality among threads (where such sharing may at first seem detrimental). In our proposal, warps within a thread block share a common block-wide stack for divergence handling. At a divergent branch, threads are compacted into new warps in hardware. Our simulation results show that this compaction mechanism provides an average speedup of 22 over a baseline per-warp, stack-based reconvergence mechanism, and 17 versus dynamic warp formation on a set of CUDA applications that suffer significantly from control flow divergence. Time-tiling is necessary for the efficient execution of iterative stencil computations. Classical hyper-rectangular tiles cannot be used due to the combination of backward and forward dependences along space dimensions. Existing techniques trade temporal data reuse for inefficiencies in other areas, such as load imbalance, redundant computations, or increased control flow overhead, therefore making it challenging for use with GPUs. We propose a time-tiling method for iterative stencil computations on GPUs. Our method does not involve redundant computations. It favors coalesced global-memory accesses, data reuse in local shared-memory or cache, avoidance of thread divergence, and concurrency, combining hexagonal tile shapes along the time and one spatial dimension with classical tiling along the other spatial dimensions. Hexagonal tiles expose multi-level parallelism as well as data reuse. Experimental results demonstrate significant performance improvements over existing stencil compilers.