Application-Specific Number Representation

Reconfigurable devices, such as Field Programmable Gate Arrays (FPGAs), enable application- specific number representations. Well-known number formats include fixed-point, floating- point, logarithmic number system (LNS), and residue number system (RNS). Such different number representations lead to different arithmetic designs and error behaviours, thus produc- ing implementations with different performance, accuracy, and cost. To investigate the design options in number representations, the first part of this thesis presents a platform that enables automated exploration of the number representation design space. The second part of the thesis shows case studies that optimise the designs for area, latency or throughput from the perspective of number representations. Automated design space exploration in the first part addresses the following two major issues: ² Automation requires arithmetic unit generation. This thesis provides optimised arithmetic library generators for logarithmic and residue arithmetic units, which support a wide range of bit widths and achieve significant improvement over previous designs. ² Generation of arithmetic units requires specifying the bit widths for each variable. This thesis describes an automatic bit-width optimisation tool called R-Tool, which combines dynamic and static analysis methods, and supports different number systems (fixed-point, floating-point, and LNS numbers). Putting it all together, the second part explores the effects of application-specific number representation on practical benchmarks, such as radiative Monte Carlo simulation, and seismic imaging computations. Experimental results show that customising the number representations brings benefits to hardware implementations: by selecting a more appropriate number format, we can reduce the area cost by up to 73.5% and improve the throughput by 14.2% to 34.1%; by performing the bit-width optimisation, we can further reduce the area cost by 9.7% to 17.3%. On the performance side, hardware implementations with customised number formats achieve 5 to potentially over 40 times speedup over software implementations

PGPG: An Automatic Generator of Pipeline Design for Programmable GRAPE Systems

We have developed PGPG (Pipeline Generator for Programmable GRAPE), a software which generates the low-level design of the pipeline processor and communication software for FPGA-based computing engines (FBCEs). An FBCE typically consists of one or multiple FPGA (Field-Programmable Gate Array) chips and local memory. Here, the term "Field-Programmable" means that one can rewrite the logic implemented to the chip after the hardware is completed, and therefore a single FBCE can be used for calculation of various functions, for example pipeline processors for gravity, SPH interaction, or image processing. The main problem with FBCEs is that the user need to develop the detailed hardware design for the processor to be implemented to FPGA chips. In addition, she or he has to write the control logic for the processor, communication and data conversion library on the host processor, and application program which uses the developed processor. These require detailed knowledge of hardware design, a hardware description language such as VHDL, the operating system and the application, and amount of human work is huge. A relatively simple design would require 1 person-year or more. The PGPG software generates all necessary design descriptions, except for the application software itself, from a high-level design description of the pipeline processor in the PGPG language. The PGPG language is a simple language, specialized to the description of pipeline processors. Thus, the design of pipeline processor in PGPG language is much easier than the traditional design. For real applications such as the pipeline for gravitational interaction, the pipeline processor generated by PGPG achieved the performance similar to that of hand-written code. In this paper we present a detailed description of PGPG version 1.0.Comment: 24 pages, 6 figures, accepted PASJ 2005 July 2

Power-Aware Design Methodologies for FPGA-Based Implementation of Video Processing Systems

The increasing capacity and capabilities of FPGA devices in recent years provide an attractive option for performance-hungry applications in the image and video processing domain. FPGA devices are often used as implementation platforms for image and video processing algorithms for real-time applications due to their programmable structure that can exploit inherent spatial and temporal parallelism. While performance and area remain as two main design criteria, power consumption has become an important design goal especially for mobile devices. Reduction in power consumption can be achieved by reducing the supply voltage, capacitances, clock frequency and switching activities in a circuit. Switching activities can be reduced by architectural optimization of the processing cores such as adders, multipliers, multiply and accumulators (MACS), etc. This dissertation research focuses on reducing the switching activities in digital circuits by considering data dependencies in bit level, word level and block level neighborhoods in a video frame. The bit level data neighborhood dependency consideration for power reduction is illustrated in the design of pipelined array, Booth and log-based multipliers. For an array multiplier, operands of the multipliers are partitioned into higher and lower parts so that the probability of the higher order parts being zero or one increases. The gating technique for the pipelined approach deactivates part(s) of the multiplier when the above special values are detected. For the Booth multiplier, the partitioning and gating technique is integrated into the Booth recoding scheme. In addition, a delay correction strategy is developed for the Booth multiplier to reduce the switching activities of the sign extension part in the partial products. A novel architecture design for the computation of log and inverse-log functions for the reduction of power consumption in arithmetic circuits is also presented. This also utilizes the proposed partitioning and gating technique for further dynamic power reduction by reducing the switching activities. The word level and block level data dependencies for reducing the dynamic power consumption are illustrated by presenting the design of a 2-D convolution architecture. Here the similarities of the neighboring pixels in window-based operations of image and video processing algorithms are considered for reduced switching activities. A partitioning and detection mechanism is developed to deactivate the parallel architecture for window-based operations if higher order parts of the pixel values are the same. A neighborhood dependent approach (NDA) is incorporated with different window buffering schemes. Consideration of the symmetry property in filter kernels is also applied with the NDA method for further reduction of switching activities. The proposed design methodologies are implemented and evaluated in a FPGA environment. It is observed that the dynamic power consumption in FPGA-based circuit implementations is significantly reduced in bit level, data level and block level architectures when compared to state-of-the-art design techniques. A specific application for the design of a real-time video processing system incorporating the proposed design methodologies for low power consumption is also presented. An image enhancement application is considered and the proposed partitioning and gating, and NDA methods are utilized in the design of the enhancement system. Experimental results show that the proposed multi-level power aware methodology achieves considerable power reduction. Research work is progressing In utilizing the data dependencies in subsequent frames in a video stream for the reduction of circuit switching activities and thereby the dynamic power consumption

Multipartite table methods

International audienceA unified view of most previous table-lookup-and-addition methods (bipartite tables, SBTM, STAM, and multipartite methods) is presented. This unified view allows a more accurate computation of the error entailed by these methods, which enables a wider design space exploration, leading to tables smaller than the best previously published ones by up to 50 percent. The synthesis of these multipartite architectures on Virtex FPGAs is also discussed. Compared to other methods involving multipliers, the multipartite approach offers the best speed/area tradeoff for precisions up to 16 bits. A reference implementation is available at www.ens-lyon.fr/LIP/Arenaire/

Hardware acceleration of photon mapping

PhD ThesisThe quest for realism in computer-generated graphics has yielded a range of algorithmic techniques, the most advanced of which are capable of rendering images at close to photorealistic quality. Due to the realism available, it is now commonplace that computer graphics are used in the creation of movie sequences, architectural renderings, medical imagery and product visualisations. This work concentrates on the photon mapping algorithm [1, 2], a physically based global illumination rendering algorithm. Photon mapping excels in producing highly realistic, physically accurate images. A drawback to photon mapping however is its rendering times, which can be significantly longer than other, albeit less realistic, algorithms. Not surprisingly, this increase in execution time is associated with a high computational cost. This computation is usually performed using the general purpose central processing unit (CPU) of a personal computer (PC), with the algorithm implemented as a software routine. Other options available for processing these algorithms include desktop PC graphics processing units (GPUs) and custom designed acceleration hardware devices. GPUs tend to be efficient when dealing with less realistic rendering solutions such as rasterisation, however with their recent drive towards increased programmability they can also be used to process more realistic algorithms. A drawback to the use of GPUs is that these algorithms often have to be reworked to make optimal use of the limited resources available. There are very few custom hardware devices available for acceleration of the photon mapping algorithm. Ray-tracing is the predecessor to photon mapping, and although not capable of producing the same physical accuracy and therefore realism, there are similarities between the algorithms. There have been several hardware prototypes, and at least one commercial offering, created with the goal of accelerating ray-trace rendering [3]. However, properties making many of these proposals suitable for the acceleration of ray-tracing are not shared by photon mapping. There are even fewer proposals for acceleration of the additional functions found only in photon mapping. All of these approaches to algorithm acceleration offer limited scalability. GPUs are inherently difficult to scale, while many of the custom hardware devices available thus far make use of large processing elements and complex acceleration data structures. In this work we make use of three novel approaches in the design of highly scalable specialised hardware structures for the acceleration of the photon mapping algorithm. Increased scalability is gained through: • The use of a brute-force approach in place of the commonly used smart approach, thus eliminating much data pre-processing, complex data structures and large processing units often required. • The use of Logarithmic Number System (LNS) arithmetic computation, which facilitates a reduction in processing area requirement. • A novel redesign of the photon inclusion test, used within the photon search method of the photon mapping algorithm. This allows an intelligent memory structure to be used for the search. The design uses two hardware structures, both of which accelerate one core rendering function. Renderings produced using field programmable gate array (FPGA) based prototypes are presented, along with details of 90nm synthesised versions of the designs which show that close to an orderof- magnitude speedup over a software implementation is possible. Due to the scalable nature of the design, it is likely that any advantage can be maintained in the face of improving processor speeds. Significantly, due to the brute-force approach adopted, it is possible to eliminate an often-used software acceleration method. This means that the device can interface almost directly to a frontend modelling package, minimising much of the pre-processing required by most other proposals

Fast fixed-point bicubic interpolation algorithm on FPGA

We propose a fast fixed-point algorithm for bicubic interpolation on FPGA. Bicubic interpolation algorithms on FPGA are mainly used in image processing systems and based on floating-point calculation. In these systems, calculations are synchronized with the frame rate and reduction of computation time is achieved designing a particular hardware architecture. Our system is intended to work with images or other similar applications like industrial control systems. The fast and energy efficient calculation is achieved using a fixed-point implementation. We obtained a maximum frequency of 27.26 MHz, a relative quantization error of 0.36% with the fractional number of bits being 7, logic utilization of 8%, and about 30% of energy saving in comparison with a C-program on the embedded HPS for the popular Matlab test function Peaks(25,25) data on SoCkit development kit (Terasic), chip: Cyclone V, 5CSXFC6D6F31C8. The experiments confirm the feasibility of the proposed method.fi=vertaisarvioitu|en=peerReviewed

Algorithms and architectures for decimal transcendental function computation

Nowadays, there are many commercial demands for decimal floating-point (DFP) arithmetic operations such as financial analysis, tax calculation, currency conversion, Internet based applications, and e-commerce. This trend gives rise to further development on DFP arithmetic units which can perform accurate computations with exact decimal operands. Due to the significance of DFP arithmetic, the IEEE 754-2008 standard for floating-point arithmetic includes it in its specifications. The basic decimal arithmetic unit, such as decimal adder, subtracter, multiplier, divider or square-root unit, as a main part of a decimal microprocessor, is attracting more and more researchers' attentions. Recently, the decimal-encoded formats and DFP arithmetic units have been implemented in IBM's system z900, POWER6, and z10 microprocessors. Increasing chip densities and transistor count provide more room for designers to add more essential functions on application domains into upcoming microprocessors. Decimal transcendental functions, such as DFP logarithm, antilogarithm, exponential, reciprocal and trigonometric, etc, as useful arithmetic operations in many areas of science and engineering, has been specified as the recommended arithmetic in the IEEE 754-2008 standard. Thus, virtually all the computing systems that are compliant with the IEEE 754-2008 standard could include a DFP mathematical library providing transcendental function computation. Based on the development of basic decimal arithmetic units, more complex DFP transcendental arithmetic will be the next building blocks in microprocessors. In this dissertation, we researched and developed several new decimal algorithms and architectures for the DFP transcendental function computation. These designs are composed of several different methods: 1) the decimal transcendental function computation based on the table-based first-order polynomial approximation method; 2) DFP logarithmic and antilogarithmic converters based on the decimal digit-recurrence algorithm with selection by rounding; 3) a decimal reciprocal unit using the efficient table look-up based on Newton-Raphson iterations; and 4) a first radix-100 division unit based on the non-restoring algorithm with pre-scaling method. Most decimal algorithms and architectures for the DFP transcendental function computation developed in this dissertation have been the first attempt to analyze and implement the DFP transcendental arithmetic in order to achieve faithful results of DFP operands, specified in IEEE 754-2008. To help researchers evaluate the hardware performance of DFP transcendental arithmetic units, the proposed architectures based on the different methods are modeled, verified and synthesized using FPGAs or with CMOS standard cells libraries in ASIC. Some of implementation results are compared with those of the binary radix-16 logarithmic and exponential converters; recent developed high performance decimal CORDIC based architecture; and Intel's DFP transcendental function computation software library. The comparison results show that the proposed architectures have significant speed-up in contrast to the above designs in terms of the latency. The algorithms and architectures developed in this dissertation provide a useful starting point for future hardware-oriented DFP transcendental function computation researches