LOCOFloat: A low-cost floating-point format for FPGAs.: Application to HIL simulators

One of the main decisions when making a digital design is which arithmetic is going to be used. The arithmetic determines the hardware resources needed and the latency of every operation. This is especially important in real-time applications like HIL (Hardware-in-the-loop), where a real-time simulation of a plant—power converter, mechanical system, or any other complex system—is accomplished. While a fixed-point gets optimal implementations, using considerably fewer resources and allowing smaller simulation steps, its use is very restricted to very specific applications, as its design effort is quite high. On the other side, IEEE-754 floating-point may have resolution problems in case of the 32-bit version, and excessive hardware usage in case of the 64-bit version. This paper presents LOCOFloat, a low-cost floating-point format designed for FPGA applications. Its key features are soft normalization of the results, using significand and exponent fields in two’s complement. This paper shows the implementation of addition, subtraction and multiplication of the proposed format. Both IEEE-754 versions and LOCOFloat are compared in this paper, implementing a HIL model of a buck converter. Although the application example is a HIL simulator, other applications could take benefit from the proposed format. Results show that LOCOFloat is as accurate as 64-bit floating-point, while reducing the use of DSPs blocks by 84%

High-performance acceleration of 2-D and 3D CNNs on FPGAs using static block floating point

Over the past few years, 2-D convolutional neural networks (CNNs) have demonstrated their great success in a wide range of 2-D computer vision applications, such as image classification and object detection. At the same time, 3-D CNNs, as a variant of 2-D CNNs, have shown their excellent ability to analyze 3-D data, such as video and geometric data. However, the heavy algorithmic complexity of 2-D and 3-D CNNs imposes a substantial overhead over the speed of these networks, which limits their deployment in real-life applications. Although various domain-specific accelerators have been proposed to address this challenge, most of them only focus on accelerating 2-D CNNs, without considering their computational efficiency on 3-D CNNs. In this article, we propose a unified hardware architecture to accelerate both 2-D and 3-D CNNs with high hardware efficiency. Our experiments demonstrate that the proposed accelerator can achieve up to 92.4% and 85.2% multiply-accumulate efficiency on 2-D and 3-D CNNs, respectively. To improve the hardware performance, we propose a hardware-friendly quantization approach called static block floating point (BFP), which eliminates the frequent representation conversions required in traditional dynamic BFP arithmetic. Comparing with the integer linear quantization using zero-point, the static BFP quantization can decrease the logic resource consumption of the convolutional kernel design by nearly 50% on a field-programmable gate array (FPGA). Without time-consuming retraining, the proposed static BFP quantization is able to quantize the precision to 8-bit mantissa with negligible accuracy loss. As different CNNs on our reconfigurable system require different hardware and software parameters to achieve optimal hardware performance and accuracy, we also propose an automatic tool for parameter optimization. Based on our hardware design and optimization, we demonstrate that the proposed accelerator can achieve 3.8-5.6 times higher energy efficiency than graphics processing unit (GPU) implementation. Comparing with the state-of-the-art FPGA-based accelerators, our design achieves higher generality and up to 1.4-2.2 times higher resource efficiency on both 2-D and 3-D CNNs

Floating-point exponential functions for DSP-enabled FPGAs

International audienceThis article presents a floating-point exponential operator generator targeting recent FPGAs with embedded memories and DSP blocks. A single-precision operator consumes just one DSP block, 18Kbits of dual-port memory, and 392 slices on Virtex-4. For larger precisions, a generic approach based on polynomial approximation is used and proves more resource-efficient than the literature. For instance a double-precision operator consumes 5 BlockRAM and 12 DSP48 blocks on Virtex-5, or 10 M9k and 22 18x18 multipliers on Stratix III. This approach is flexible, scales well beyond double-precision, and enables frequencies close to the FPGA's nominal frequency. All the proposed architectures are last-bit accurate for all the floating-point range.They are available in the open-source FloPoCo framework

Customizing floating-point units for FPGAs: Area-performance-standard trade-offs

The high integration density of current nanometer technologies allows the implementation of complex floating-point applications in a single FPGA. In this work the intrinsic complexity of floating-point operators is addressed targeting configurable devices and making design decisions providing the most suitable performance-standard compliance trade-offs. A set of floating-point libraries composed of adder/subtracter, multiplier, divisor, square root, exponential, logarithm and power function are presented. Each library has been designed taking into account special characteristics of current FPGAs, and with this purpose we have adapted the IEEE floating-point standard (software-oriented) to a custom FPGA-oriented format. Extended experimental results validate the design decisions made and prove the usefulness of reducing the format complexit

Accuracy, Cost and Performance Trade-Offs for Streaming Set-Wise Floating Point Accumulation on FPGAs

The set-wise summation operation is perhaps one of the most fundamental and widely used operations in scientific applications. In these applications, maintaining the accuracy of the summation is also important as floating point operations have inherent errors associated with them. Designing floating-point accumulators presents a unique set of challenges: double-precision addition is usually deeply pipelined and without special micro-architectural or data scheduling techniques, the data hazard that exists. There have been several efforts to design floating point accumulators and accurate summation architecture using different algorithms on FPGAs but these problems have been dealt with separately. In this dissertation, we present a general purpose reduction circuit architecture which addresses the issues of data hazard and accuracy in set-wise floating point summation. The reduction circuit architecture is parametrizable and can be scaled according to the depth of the adder pipeline. Also, the dynamic scheduling logic we use in this makes it highly resource efficient. Further, the resource requirements for this design are low. We also study various methods to improve the accuracy of summation of floating point numbers. We have implemented four designs. The reduction circuit architecture serves as the framework for these designs. Two of the designs namely AEC and AECSA are based on compensated summation while the two designs called EPRC80 and EPRC128 implement set-wise floating point accumulation in extended precision. We present and compare the accuracy and cost- operating frequency and resource requirements- tradeoffs associated with these designs. On the basis of our experiments, we find that these designs achieve significantly better accuracy. Three of the designs– AEC, EPRC80 and EPRC128– operate at around 180MHz on Xilinx Virtex 5 FPGA which is comparable to the reduction circuit while AECSA operates at 28% less frequency. The increase in resource requirement ranges from 41% to 320%. We conclude that accuracy can be achieved at the expense of more resources but the operating frequency can be maintained

Design of efficient reversible floating-point arithmetic unit on field programmable gate array platform and its performance analysis

The reversible logic gates are used to improve the power dissipation in modern computer applications. The floating-point numbers with reversible features are added advantage to performing complex algorithms with high-performance computations. This manuscript implements an efficient reversible floating-point arithmetic (RFPA) unit, and its performance metrics are realized in detail. The RFP adder/subtractor (A/S), RFP multiplier, and RFP divider units are designed as a part of the RFP arithmetic unit. The RFPA unit is designed by considering basic reversible gates. The mantissa part of the RFP multiplier is created using a 24x24 Wallace tree multiplier. In contrast, the reciprocal unit of the RFP divider is designed using Newton Raphson’s method. The RFPA unit and its submodules are executed in parallel by utilizing one clock cycle individually. The RFPA unit and its submodules are synthesized separately on the Vivado IDE environment and obtained the implementation results on Artix-7 field programmable gate array (FPGA). The RFPA unit utilizes only 18.44% slice look-up tables (LUTs) by consuming the 0.891 W total power on Artix-7 FPGA. The RFPA unit sub-models are compared with existing approaches with better performance metrics and chip resource utilization improvements

Flexible Multiple-Precision Fused Arithmetic Units for Efficient Deep Learning Computation

Deep Learning has achieved great success in recent years. In many fields of applications, such as computer vision, biomedical analysis, and natural language processing, deep learning can achieve a performance that is even better than human-level. However, behind this superior performance is the expensive hardware cost required to implement deep learning operations. Deep learning operations are both computation intensive and memory intensive. Many research works in the literature focused on improving the efficiency of deep learning operations. In this thesis, special focus is put on improving deep learning computation and several efficient arithmetic unit architectures are proposed and optimized for deep learning computation. The contents of this thesis can be divided into three parts: (1) the optimization of general-purpose arithmetic units for deep learning computation; (2) the design of deep learning specific arithmetic units; (3) the optimization of deep learning computation using 3D memory architecture. Deep learning models are usually trained on graphics processing unit (GPU) and the computations are done with single-precision floating-point numbers. However, recent works proved that deep learning computation can be accomplished with low precision numbers. The half-precision numbers are becoming more and more popular in deep learning computation due to their lower hardware cost compared to the single-precision numbers. In conventional floating-point arithmetic units, single-precision and beyond are well supported to achieve a better precision. However, for deep learning computation, since the computations are intensive, low precision computation is desired to achieve better throughput. As the popularity of half-precision raises, half-precision operations are also need to be supported. Moreover, the deep learning computation contains many dot-product operations and therefore, the support of mixed-precision dot-product operations can be explored in a multiple-precision architecture. In this thesis, a multiple-precision fused multiply-add (FMA) architecture is proposed. It supports half/single/double/quadruple-precision FMA operations. In addition, it also supports 2-term mixed-precision dot-product operations. Compared to the conventional multiple-precision FMA architecture, the newly added half-precision support and mixed-precision dot-product only bring minor resource overhead. The proposed FMA can be used as general-purpose arithmetic unit. Due to the support of parallel half-precision computations and mixed-precision dot-product computations, it is especially suitable for deep learning computation. For the design of deep learning specific computation unit, more optimizations can be performed. First, a fixed-point and floating-point merged multiply-accumulate (MAC) unit is proposed. As deep learning computation can be accomplished with low precision number formats, the support of high precision floating-point operations can be eliminated. In this design, the half-precision floating-point format is supported to provide a large dynamic range to handle small gradients for deep learning training. For deep learning inference, 8-bit fixed-point 2-term dot-product computation is supported. Second, a flexible multiple-precision MAC unit architecture is proposed. The proposed MAC unit supports both fixed-point operations and floating-point operations. For floating-point format, the proposed unit supports one 16-bit MAC operation or sum of two 8-bit multiplications plus a 16-bit addend. To make the proposed MAC unit more versatile, the bit-width of exponent and mantissa can be flexibly exchanged. By setting the bit-width of exponent to zero, the proposed MAC unit also supports fixed-point operations. For fixed-point format, the proposed unit supports one 16-bit MAC or sum of two 8-bit multiplications plus a 16-bit addend. Moreover, the proposed unit can be further divided to support sum of four 4-bit multiplications plus a 16-bit addend. At the lowest precision, the proposed MAC unit supports accumulating of eight 1-bit logic AND operations to enable the support of binary neural networks. Finally, a MAC architecture based on the posit format, a promising numerical format in deep learning computation, is proposed to facilitate the use of posit format in deep learning computation. In addition to the above mention arithmetic units, an improved hybrid memory cube (HMC) architecture is proposed for weight-sharing deep neural network processing. By modifying the HMC instruction set and HMC logic layer, the major part of the deep learning computation can be accomplished inside memory. The proposed design reduces the memory bandwidth requirements and thus reduces the energy consumed by memory data transfer

Numerical solutions of differential equations on FPGA-enhanced computers

Conventionally, to speed up scientific or engineering (S&E) computation programs on general-purpose computers, one may elect to use faster CPUs, more memory, systems with more efficient (though complicated) architecture, better software compilers, or even coding with assembly languages. With the emergence of Field Programmable Gate Array (FPGA) based Reconfigurable Computing (RC) technology, numerical scientists and engineers now have another option using FPGA devices as core components to address their computational problems. The hardware-programmable, low-cost, but powerful “FPGA-enhanced computer” has now become an attractive approach for many S&E applications. A new computer architecture model for FPGA-enhanced computer systems and its detailed hardware implementation are proposed for accelerating the solutions of computationally demanding and data intensive numerical PDE problems. New FPGAoptimized algorithms/methods for rapid executions of representative numerical methods such as Finite Difference Methods (FDM) and Finite Element Methods (FEM) are designed, analyzed, and implemented on it. Linear wave equations based on seismic data processing applications are adopted as the targeting PDE problems to demonstrate the effectiveness of this new computer model. Their sustained computational performances are compared with pure software programs operating on commodity CPUbased general-purpose computers. Quantitative analysis is performed from a hierarchical set of aspects as customized/extraordinary computer arithmetic or function units, compact but flexible system architecture and memory hierarchy, and hardwareoptimized numerical algorithms or methods that may be inappropriate for conventional general-purpose computers. The preferable property of in-system hardware reconfigurability of the new system is emphasized aiming at effectively accelerating the execution of complex multi-stage numerical applications. Methodologies for accelerating the targeting PDE problems as well as other numerical PDE problems, such as heat equations and Laplace equations utilizing programmable hardware resources are concluded, which imply the broad usage of the proposed FPGA-enhanced computers

Custom optimization algorithms for efficient hardware implementation

The focus is on real-time optimal decision making with application in advanced control systems. These computationally intensive schemes, which involve the repeated solution of (convex) optimization problems within a sampling interval, require more efficient computational methods than currently available for extending their application to highly dynamical systems and setups with resource-constrained embedded computing platforms. A range of techniques are proposed to exploit synergies between digital hardware, numerical analysis and algorithm design. These techniques build on top of parameterisable hardware code generation tools that generate VHDL code describing custom computing architectures for interior-point methods and a range of first-order constrained optimization methods. Since memory limitations are often important in embedded implementations we develop a custom storage scheme for KKT matrices arising in interior-point methods for control, which reduces memory requirements significantly and prevents I/O bandwidth limitations from affecting the performance in our implementations. To take advantage of the trend towards parallel computing architectures and to exploit the special characteristics of our custom architectures we propose several high-level parallel optimal control schemes that can reduce computation time. A novel optimization formulation was devised for reducing the computational effort in solving certain problems independent of the computing platform used. In order to be able to solve optimization problems in fixed-point arithmetic, which is significantly more resource-efficient than floating-point, tailored linear algebra algorithms were developed for solving the linear systems that form the computational bottleneck in many optimization methods. These methods come with guarantees for reliable operation. We also provide finite-precision error analysis for fixed-point implementations of first-order methods that can be used to minimize the use of resources while meeting accuracy specifications. The suggested techniques are demonstrated on several practical examples, including a hardware-in-the-loop setup for optimization-based control of a large airliner.Open Acces