Floating-Point Matrix Product on FPGA

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High-level synthesis optimization for blocked floating-point matrix multiplication

In the last decade floating-point matrix multiplication on FPGAs has been studied extensively and efficient architectures as well as detailed performance models have been developed. By design these IP cores take a fixed footprint which not necessarily optimizes the use of all available resources. Moreover, the low-level architectures are not easily amenable to a parameterized synthesis. In this paper high-level synthesis is used to fine-tune the configuration parameters in order to achieve the highest performance with maximal resource utilization. An\ exploration strategy is presented to optimize the use of critical resources (DSPs, memory) for any given FPGA. To account for the limited memory size on the FPGA, a block-oriented matrix multiplication is organized such that the block summation is done on the CPU while the block multiplication occurs on the logic fabric simultaneously. The communication overhead between the CPU and the FPGA is minimized by streaming the blocks in a Gray code ordering scheme which maximizes the data reuse for consecutive block matrix product calculations. Using high-level synthesis optimization, the programmable logic operates at 93% of the theoretical peak performance and the combined CPU-FPGA design achieves 76% of the available hardware processing speed for the floating-point multiplication of 2K by 2K matrices

A general framework for efficient FPGA implementation of matrix product

Original article can be found at: http://www.medjcn.com/ Copyright Softmotor LimitedHigh performance systems are required by the developers for fast processing of computationally intensive applications. Reconfigurable hardware devices in the form of Filed-Programmable Gate Arrays (FPGAs) have been proposed as viable system building blocks in the construction of high performance systems at an economical price. Given the importance and the use of matrix algorithms in scientific computing applications, they seem ideal candidates to harness and exploit the advantages offered by FPGAs. In this paper, a system for matrix algorithm cores generation is described. The system provides a catalog of efficient user-customizable cores, designed for FPGA implementation, ranging in three different matrix algorithm categories: (i) matrix operations, (ii) matrix transforms and (iii) matrix decomposition. The generated core can be either a general purpose or a specific application core. The methodology used in the design and implementation of two specific image processing application cores is presented. The first core is a fully pipelined matrix multiplier for colour space conversion based on distributed arithmetic principles while the second one is a parallel floating-point matrix multiplier designed for 3D affine transformations.Peer reviewe

FINN: A Framework for Fast, Scalable Binarized Neural Network Inference

Research has shown that convolutional neural networks contain significant redundancy, and high classification accuracy can be obtained even when weights and activations are reduced from floating point to binary values. In this paper, we present FINN, a framework for building fast and flexible FPGA accelerators using a flexible heterogeneous streaming architecture. By utilizing a novel set of optimizations that enable efficient mapping of binarized neural networks to hardware, we implement fully connected, convolutional and pooling layers, with per-layer compute resources being tailored to user-provided throughput requirements. On a ZC706 embedded FPGA platform drawing less than 25 W total system power, we demonstrate up to 12.3 million image classifications per second with 0.31 {\mu}s latency on the MNIST dataset with 95.8% accuracy, and 21906 image classifications per second with 283 {\mu}s latency on the CIFAR-10 and SVHN datasets with respectively 80.1% and 94.9% accuracy. To the best of our knowledge, ours are the fastest classification rates reported to date on these benchmarks.Comment: To appear in the 25th International Symposium on Field-Programmable Gate Arrays, February 201

Efficiency analysis methodology of FPGAs based on lost frequencies, area and cycles

We propose a methodology to study and to quantify efficiency and the impact of overheads on runtime performance. Most work on High-Performance Computing (HPC) for FPGAs only studies runtime performance or cost, while we are interested in how far we are from peak performance and, more importantly, why. The efficiency of runtime performance is defined with respect to the ideal computational runtime in absence of inefficiencies. The analysis of the difference between actual and ideal runtime reveals the overheads and bottlenecks. A formal approach is proposed to decompose the efficiency into three components: frequency, area and cycles. After quantification of the efficiencies, a detailed analysis has to reveal the reasons for the lost frequencies, lost area and lost cycles. We propose a taxonomy of possible causes and practical methods to identify and quantify the overheads. The proposed methodology is applied on a number of use cases to illustrate the methodology. We show the interaction between the three components of efficiency and show how bottlenecks are revealed

Implementation of the K-Means Algorithm on Heterogeneous Devices: A Use Case Based on an Industrial Dataset

This paper presents and analyzes a heterogeneous implementation of an industrial use case based on K-means that targets symmetric multiprocessing (SMP), GPUs and FPGAs. We present how the application can be optimized from an algorithmic point of view and how this optimization performs on two heterogeneous platforms. The presented implementation relies on the OmpSs programming model, which introduces a simplified pragma-based syntax for the communication between the main processor and the accelerators. Performance improvement can be achieved by the programmer explicitly specifying the data memory accesses or copies. As expected, the newer SMP+GPU system studied is more powerful than the older SMP+FPGA system. However the latter is enough to fulfill the requirements of our use case and we show that uses less energy when considering only the active power of the execution.This work is partially supported by the European Union H2020 project AXIOM (grant agreement n. 645496), HiPEAC (grant agreement n. 687698), and Mont-Blanc (grant agreements n. 288777, 610402 and 671697), the Spanish Government Programa Severo Ochoa (SEV-2015-0493), the Spanish Ministry of Science and Technology (TIN2015- 65316-P) and the Departament d’Innovació, Universitats i Empresa de la Generalitat de Catalunya, under project MPEXPAR: Models de Programaci´o i Entorns d’Execució Paral·lels (2014-SGR-1051).Peer ReviewedPostprint (author's final draft