CORDICのハードウェア構成及び応用に関する研究

電気通信大学201

Efficient floating-point givens rotation unit

This is a post-peer-review, pre-copyedit version of an article published in Circuits, Systems, and Signal Processing.High-throughput QR decomposition is a key operation in many advanced signal processing and communication applications. For some of these applications, using floating-point computation is becoming almost compulsory. However, there are scarce works in hardware implementations of floating-point QR decomposition for embedded systems. In this paper, we propose a very efficient high-throughput floating-point Givens rotation unit for QR decomposition. Moreover, the initial proposed design for conventional number formats is enhanced by using the new Half-Unit Biased format. The provided error analysis shows the effectiveness of our proposals and the trade-off of different implementation parameters. We also present FPGA implementation results and a thorough comparison between both approaches. These implementation results also reveal outstanding improvements compared to other previous similar designs in terms of area, latency, and throughput.This work was supported in part by following Spanish projects: TIN2016-80920-R, and JA2012 P12-TIC-169

Profile-directed specialisation of custom floating-point hardware

We present a methodology for generating floating-point arithmetic hardware designs which are, for suitable applications, much reduced in size, while still retaining performance and IEEE-754 compliance. Our system uses three key parts: a profiling tool, a set of customisable floating-point units and a selection of system integration methods. We use a profiling tool for floating-point behaviour to identify arithmetic operations where fundamental elements of IEEE-754 floating-point may be compromised, without generating erroneous results in the common case. In the uncommon case, we use simple detection logic to determine when operands lie outside the range of capabilities of the optimised hardware. Out-of-range operations are handled by a separate, fully capable, floatingpoint implementation, either on-chip or by returning calculations to a host processor. We present methods of system integration to achieve this errorcorrection. Thus the system suffers no compromise in IEEE-754 compliance, even when the synthesised hardware would generate erroneous results. In particular, we identify from input operands the shift amounts required for input operand alignment and post-operation normalisation. For operations where these are small, we synthesise hardware with reduced-size barrel-shifters. We also propose optimisations to take advantage of other profile-exposed behaviours, including removing the hardware required to swap operands in a floating-point adder or subtractor, and reducing the exponent range to fit observed values. We present profiling results for a range of applications, including a selection of computational science programs, Spec FP 95 benchmarks and the FFMPEG media processing tool, indicating which would be amenable to our method. Selected applications which demonstrate potential for optimisation are then taken through to a hardware implementation. We show up to a 45% decrease in hardware size for a floating-point datapath, with a correctable error-rate of less then 3%, even with non-profiled datasets

Novel load identification techniques and a steady state self-tuning prototype for switching mode power supplies

Control of Switched Mode Power Supplies (SMPS) has been traditionally achieved through analog means with dedicated integrated circuits (ICs). However, as power systems are becoming increasingly complex, the classical concept of control has gradually evolved into the more general problem of power management, demanding functionalities that are hardly achievable in analog controllers. The high flexibility offered by digital controllers and their capability to implement sophisticated control strategies, together with the programmability of controller parameters, make digital control very attractive as an option for improving the features of dcdc converters. On the other side, digital controllers find their major weak point in the achievable dynamic performances of the closed loop system. Indeed, analogto-digital conversion times, computational delays and sampling-related delays strongly limit the small signal closed loop bandwidth of a digitally controlled SMPS. Quantization effects set other severe constraints not known to analog solutions. For these reasons, intensive scientific research activity is addressing the problem of making digital compensator stronger competitors against their analog counterparts in terms of achievable performances. In a wide range of applications, dcdc converters with high efficiency over the whole range of their load values are required. Integrated digital controllers for Switching Mode Power Supplies are gaining growing interest, since it has been shown the feasibility of digital controller ICs specifically developed for high frequency switching converters. One very interesting potential benefit is the use of autotuning of controller parameters (on-line controllers), so that the dynamic response can be set at the software level, independently of output capacitor filters, component variations and ageing. These kind of algorithms are able to identify the output filter configuration (system identification) and then automatically compute the best compensator gains to adjust system margins and bandwidth. In order to be an interesting solution, however, the self-tuning should satisfy two important requirements: it should not heavily affect converter operation under nominal condition and it should be based on a simple and robust algorithm whose complexity does not require a significant increase of the silicon area of the IC controller. The first issue is avoided performing the system identification (SI) with the system open loop configuration, where perturbations can be induced in the system before the start up. Much more challenging is to satisfy this requirement during steady state operations, where perturbations on the output voltage are limited by the regular operations of the converter. The main advantage of steady state SI methods, is the detection of possible non-idealities occurring during the converter operations. In this way, the system dynamics can be consequently adjusted with the compensator parameters tuning. The resource saving issue, requires the development of äd-hocßelf-tuning techniques specifically tailored for integrated digitally controlled converters. Considering the flexibility of digital control, self-tuning algorithms can be studied and easily integrated at hardware level into closed loop SMPS reducing development time and R & D costs. The work of this dissertation finds its origin in this context. Smart power management is accomplished by tuning the controller parameters accordingly to the identified converter configuration. Themain difficult for self-tuning techniques is the identification of the converter output filter configuration. Two novel system identification techniques have been validated in this dissertation. The open loop SI method is based on the system step response, while dithering amplification effects are exploited for the steady state SI method. The open loop method can be used as autotunig approach during or before the system start up, a step evolving reference voltage has been used as system perturbation and to obtain the output filter information with the Power Spectral Density (PSD) computation of the system step response. The use of ¢§ modulator is largely increasing in digital control feedback. During the steady state, the finite resolution introduces quantization effects on the signal path causing low frequency contributes of the digital control word. Through oversampling-dithering capabilities of ¢§ modulators, resolution improvements are obtained. The presented steady state identification techniques demonstrates that, amplifying the dithering effects on the signal path, the output filter information can be obtained on the digital side by processing with the PSD computation the perturbed output voltage. The amount of noise added on the output voltage does not affect the converter operations, mathematical considerations have been addressed and then justified both with a Matlab/Simulink fixed-point and a FPGA-based closed loop system. The load output filter identification of both algorithms, refer to the frequency domain. When the respective perturbations occurs, the system response is observed on the digital side and processed with the PSD computation. The extracted parameters are the resonant frequency ans the possible ESR (Effective Series Resistance) contributes,which can be detected as maximumin the PSD output. The SI methods have been validated for different configurations of buck converters on a fixed-point closed loop model, however, they can be easily applied to further converter configurations. The steady state method has been successfully integrated into a FPGA-based prototype for digitally controlled buck converters, that integrates a PSD computer needed for the load parameters identification. At this purpose, a novel VHDL-coded full-scalable hybrid processor for Constant Geometry FFT (CG-FFT) computation has been designed and integrated into the PSD computation system. The processor is based on a variation of the conventional algorithm used for FFT, which is the Constant-Geometry FFT (CG-FFT).Hybrid CORDIC-LUT scalable architectures, has been introduced as alternative approach for the twiddle factors (phase factors) computation needed during the FFT algorithms execution. The shared core architecture uses a single phase rotator to satisfy all TF requests. It can achieve improved logic saving by trading off with computational speed. The pipelined architecture is composed of a number of stages equal to the number of PEs and achieves the highest possible throughput, at the expense of more hardware usage

Novel load identification techniques and a steady state self-tuning prototype for switching mode power supplies

Control of Switched Mode Power Supplies (SMPS) has been traditionally achieved through analog means with dedicated integrated circuits (ICs). However, as power systems are becoming increasingly complex, the classical concept of control has gradually evolved into the more general problem of power management, demanding functionalities that are hardly achievable in analog controllers. The high flexibility offered by digital controllers and their capability to implement sophisticated control strategies, together with the programmability of controller parameters, make digital control very attractive as an option for improving the features of dcdc converters. On the other side, digital controllers find their major weak point in the achievable dynamic performances of the closed loop system. Indeed, analogto-digital conversion times, computational delays and sampling-related delays strongly limit the small signal closed loop bandwidth of a digitally controlled SMPS. Quantization effects set other severe constraints not known to analog solutions. For these reasons, intensive scientific research activity is addressing the problem of making digital compensator stronger competitors against their analog counterparts in terms of achievable performances. In a wide range of applications, dcdc converters with high efficiency over the whole range of their load values are required. Integrated digital controllers for Switching Mode Power Supplies are gaining growing interest, since it has been shown the feasibility of digital controller ICs specifically developed for high frequency switching converters. One very interesting potential benefit is the use of autotuning of controller parameters (on-line controllers), so that the dynamic response can be set at the software level, independently of output capacitor filters, component variations and ageing. These kind of algorithms are able to identify the output filter configuration (system identification) and then automatically compute the best compensator gains to adjust system margins and bandwidth. In order to be an interesting solution, however, the self-tuning should satisfy two important requirements: it should not heavily affect converter operation under nominal condition and it should be based on a simple and robust algorithm whose complexity does not require a significant increase of the silicon area of the IC controller. The first issue is avoided performing the system identification (SI) with the system open loop configuration, where perturbations can be induced in the system before the start up. Much more challenging is to satisfy this requirement during steady state operations, where perturbations on the output voltage are limited by the regular operations of the converter. The main advantage of steady state SI methods, is the detection of possible non-idealities occurring during the converter operations. In this way, the system dynamics can be consequently adjusted with the compensator parameters tuning. The resource saving issue, requires the development of äd-hocßelf-tuning techniques specifically tailored for integrated digitally controlled converters. Considering the flexibility of digital control, self-tuning algorithms can be studied and easily integrated at hardware level into closed loop SMPS reducing development time and R & D costs. The work of this dissertation finds its origin in this context. Smart power management is accomplished by tuning the controller parameters accordingly to the identified converter configuration. Themain difficult for self-tuning techniques is the identification of the converter output filter configuration. Two novel system identification techniques have been validated in this dissertation. The open loop SI method is based on the system step response, while dithering amplification effects are exploited for the steady state SI method. The open loop method can be used as autotunig approach during or before the system start up, a step evolving reference voltage has been used as system perturbation and to obtain the output filter information with the Power Spectral Density (PSD) computation of the system step response. The use of ¢§ modulator is largely increasing in digital control feedback. During the steady state, the finite resolution introduces quantization effects on the signal path causing low frequency contributes of the digital control word. Through oversampling-dithering capabilities of ¢§ modulators, resolution improvements are obtained. The presented steady state identification techniques demonstrates that, amplifying the dithering effects on the signal path, the output filter information can be obtained on the digital side by processing with the PSD computation the perturbed output voltage. The amount of noise added on the output voltage does not affect the converter operations, mathematical considerations have been addressed and then justified both with a Matlab/Simulink fixed-point and a FPGA-based closed loop system. The load output filter identification of both algorithms, refer to the frequency domain. When the respective perturbations occurs, the system response is observed on the digital side and processed with the PSD computation. The extracted parameters are the resonant frequency ans the possible ESR (Effective Series Resistance) contributes,which can be detected as maximumin the PSD output. The SI methods have been validated for different configurations of buck converters on a fixed-point closed loop model, however, they can be easily applied to further converter configurations. The steady state method has been successfully integrated into a FPGA-based prototype for digitally controlled buck converters, that integrates a PSD computer needed for the load parameters identification. At this purpose, a novel VHDL-coded full-scalable hybrid processor for Constant Geometry FFT (CG-FFT) computation has been designed and integrated into the PSD computation system. The processor is based on a variation of the conventional algorithm used for FFT, which is the Constant-Geometry FFT (CG-FFT).Hybrid CORDIC-LUT scalable architectures, has been introduced as alternative approach for the twiddle factors (phase factors) computation needed during the FFT algorithms execution. The shared core architecture uses a single phase rotator to satisfy all TF requests. It can achieve improved logic saving by trading off with computational speed. The pipelined architecture is composed of a number of stages equal to the number of PEs and achieves the highest possible throughput, at the expense of more hardware usage

TransPimLib: A Library for Efficient Transcendental Functions on Processing-in-Memory Systems

Processing-in-memory (PIM) promises to alleviate the data movement bottleneck in modern computing systems. However, current real-world PIM systems have the inherent disadvantage that their hardware is more constrained than in conventional processors (CPU, GPU), due to the difficulty and cost of building processing elements near or inside the memory. As a result, general-purpose PIM architectures support fairly limited instruction sets and struggle to execute complex operations such as transcendental functions and other hard-to-calculate operations (e.g., square root). These operations are particularly important for some modern workloads, e.g., activation functions in machine learning applications. In order to provide support for transcendental (and other hard-to-calculate) functions in general-purpose PIM systems, we present \emph{TransPimLib}, a library that provides CORDIC-based and LUT-based methods for trigonometric functions, hyperbolic functions, exponentiation, logarithm, square root, etc. We develop an implementation of TransPimLib for the UPMEM PIM architecture and perform a thorough evaluation of TransPimLib's methods in terms of performance and accuracy, using microbenchmarks and three full workloads (Blackscholes, Sigmoid, Softmax). We open-source all our code and datasets at~\url{https://github.com/CMU-SAFARI/transpimlib}.Comment: Our open-source software is available at https://github.com/CMU-SAFARI/transpimli

Desarrollo de una arquitectura hardware para procesamiento especializado

El método COordinate Rotation DIgital Computer (CORDIC) es un simple algoritmo que puede calcular de forma eficiente múltiples operaciones matemáticas, como funciones trigonométricas, raíces, multiplicaciones, divisiones, etc. solamente usando sumas, restas, movimiento de bits y una pequeña Lookup Table (LUT). El auge de procesamiento con punto flotante ha hecho que se tenga que reevaluar los casos de uso del método e investigar y aportar variantes que usen este tipo de datos de forma eficiente, por lo que se ha realizado un estudio sobre las mejoras que se han ido realizando a lo largo de los 60 años y, además, se ha hecho hincapié en el posible uso de CORDIC con punto flotante. Después de realizar un estudio extenso sobre los casos de uso e investigación actual sobre CORDIC, se ha implementado tres variantes usando el lenguaje Verilog para evaluar las mejoras expuestas en los estudios expuestos anteriormente. El primero se basa en el propio método estándar, el segundo se añade pipelining y un último con una conversión a punto flotante. Tras la implementación, se ha visto una clara mejora de throughput frente al CORDIC básico, y se ha visto una mejora de precisión en CORDIC en punto flotante, con el inconveniente de aumento del número de ciclos para procesar. También se ha visto un aumento de complejidad en la implementación de punto flotante, un punto negativo a la hora de tener en cuenta que el método tiene una filosofía de simplicidad. La idea de investigar los casos de uso actuales del CORDIC viene de Antonio Jimeno-Morenilla, que fue recomendado por uno de mis tutores, Marcelo Saval Calvo. Por recomendación de Antonio, José Luis Sánchez Romero se unió como segundo tutor para ayudar en el trabajo al tener un buen conocimiento de arquitecturas y haber trabajado con CORDIC anteriormente. Agradezco a todos los profesores que me han guiado en este trabajo y ofrecido cualquier apoyo que haya necesitado

Embedded electronic systems driven by run-time reconfigurable hardware

Abstract This doctoral thesis addresses the design of embedded electronic systems based on run-time reconfigurable hardware technology –available through SRAM-based FPGA/SoC devices– aimed at contributing to enhance the life quality of the human beings. This work does research on the conception of the system architecture and the reconfiguration engine that provides to the FPGA the capability of dynamic partial reconfiguration in order to synthesize, by means of hardware/software co-design, a given application partitioned in processing tasks which are multiplexed in time and space, optimizing thus its physical implementation –silicon area, processing time, complexity, flexibility, functional density, cost and power consumption– in comparison with other alternatives based on static hardware (MCU, DSP, GPU, ASSP, ASIC, etc.). The design flow of such technology is evaluated through the prototyping of several engineering applications (control systems, mathematical coprocessors, complex image processors, etc.), showing a high enough level of maturity for its exploitation in the industry.Resumen Esta tesis doctoral abarca el diseño de sistemas electrónicos embebidos basados en tecnología hardware dinámicamente reconfigurable –disponible a través de dispositivos lógicos programables SRAM FPGA/SoC– que contribuyan a la mejora de la calidad de vida de la sociedad. Se investiga la arquitectura del sistema y del motor de reconfiguración que proporcione a la FPGA la capacidad de reconfiguración dinámica parcial de sus recursos programables, con objeto de sintetizar, mediante codiseño hardware/software, una determinada aplicación particionada en tareas multiplexadas en tiempo y en espacio, optimizando así su implementación física –área de silicio, tiempo de procesado, complejidad, flexibilidad, densidad funcional, coste y potencia disipada– comparada con otras alternativas basadas en hardware estático (MCU, DSP, GPU, ASSP, ASIC, etc.). Se evalúa el flujo de diseño de dicha tecnología a través del prototipado de varias aplicaciones de ingeniería (sistemas de control, coprocesadores aritméticos, procesadores de imagen, etc.), evidenciando un nivel de madurez viable ya para su explotación en la industria.Resum Aquesta tesi doctoral està orientada al disseny de sistemes electrònics empotrats basats en tecnologia hardware dinàmicament reconfigurable –disponible mitjançant dispositius lògics programables SRAM FPGA/SoC– que contribueixin a la millora de la qualitat de vida de la societat. S’investiga l’arquitectura del sistema i del motor de reconfiguració que proporcioni a la FPGA la capacitat de reconfiguració dinàmica parcial dels seus recursos programables, amb l’objectiu de sintetitzar, mitjançant codisseny hardware/software, una determinada aplicació particionada en tasques multiplexades en temps i en espai, optimizant així la seva implementació física –àrea de silici, temps de processat, complexitat, flexibilitat, densitat funcional, cost i potència dissipada– comparada amb altres alternatives basades en hardware estàtic (MCU, DSP, GPU, ASSP, ASIC, etc.). S’evalúa el fluxe de disseny d’aquesta tecnologia a través del prototipat de varies aplicacions d’enginyeria (sistemes de control, coprocessadors aritmètics, processadors d’imatge, etc.), demostrant un nivell de maduresa viable ja per a la seva explotació a la indústria

KAVUAKA: a low-power application-specific processor architecture for digital hearing aids

The power consumption of digital hearing aids is very restricted due to their small physical size and the available hardware resources for signal processing are limited. However, there is a demand for more processing performance to make future hearing aids more useful and smarter. Future hearing aids should be able to detect, localize, and recognize target speakers in complex acoustic environments to further improve the speech intelligibility of the individual hearing aid user. Computationally intensive algorithms are required for this task. To maintain acceptable battery life, the hearing aid processing architecture must be highly optimized for extremely low-power consumption and high processing performance.The integration of application-specific instruction-set processors (ASIPs) into hearing aids enables a wide range of architectural customizations to meet the stringent power consumption and performance requirements. In this thesis, the application-specific hearing aid processor KAVUAKA is presented, which is customized and optimized with state-of-the-art hearing aid algorithms such as speaker localization, noise reduction, beamforming algorithms, and speech recognition. Specialized and application-specific instructions are designed and added to the baseline instruction set architecture (ISA). Among the major contributions are a multiply-accumulate (MAC) unit for real- and complex-valued numbers, architectures for power reduction during register accesses, co-processors and a low-latency audio interface. With the proposed MAC architecture, the KAVUAKA processor requires 16 % less cycles for the computation of a 128-point fast Fourier transform (FFT) compared to related programmable digital signal processors. The power consumption during register file accesses is decreased by 6 %to 17 % with isolation and by-pass techniques. The hardware-induced audio latency is 34 %lower compared to related audio interfaces for frame size of 64 samples.The final hearing aid system-on-chip (SoC) with four KAVUAKA processor cores and ten co-processors is integrated as an application-specific integrated circuit (ASIC) using a 40 nm low-power technology. The die size is 3.6 mm2. Each of the processors and co-processors contains individual customizations and hardware features with a varying datapath width between 24-bit to 64-bit. The core area of the 64-bit processor configuration is 0.134 mm2. The processors are organized in two clusters that share memory, an audio interface, co-processors and serial interfaces. The average power consumption at a clock speed of 10 MHz is 2.4 mW for SoC and 0.6 mW for the 64-bit processor.Case studies with four reference hearing aid algorithms are used to present and evaluate the proposed hardware architectures and optimizations. The program code for each processor and co-processor is generated and optimized with evolutionary algorithms for operation merging,instruction scheduling and register allocation. The KAVUAKA processor architecture is com-pared to related processor architectures in terms of processing performance, average power consumption, and silicon area requirements