Pipelining Of Double Precision Floating Point Division And Square Root Operations On Field-programmable Gate Arrays

Many space applications, such as vision-based systems, synthetic aperture radar, and radar altimetry rely increasingly on high data rate DSP algorithms. These algorithms use double precision floating point arithmetic operations. While most DSP applications can be executed on DSP processors, the DSP numerical requirements of these new space applications surpass by far the numerical capabilities of many current DSP processors. Since the tradition in DSP processing has been to use fixed point number representation, only recently have DSP processors begun to incorporate floating point arithmetic units, even though most of these units handle only single precision floating point addition/subtraction, multiplication, and occasionally division. While DSP processors are slowly evolving to meet the numerical requirements of newer space applications, FPGA densities have rapidly increased to parallel and surpass even the gate densities of many DSP processors and commodity CPUs. This makes them attractive platforms to implement compute-intensive DSP computations. Even in the presence of this clear advantage on the side of FPGAs, few attempts have been made to examine how wide precision floating point arithmetic, particularly division and square root operations, can perform on FPGAs to support these compute-intensive DSP applications. In this context, this thesis presents the sequential and pipelined designs of IEEE-754 compliant double floating point division and square root operations based on low radix digit recurrence algorithms. FPGA implementations of these algorithms have the advantage of being easily testable. In particular, the pipelined designs are synthesized based on careful partial and full unrolling of the iterations in the digit recurrence algorithms. In the overall, the implementations of the sequential and pipelined designs are common-denominator implementations which do not use any performance-enhancing embedded components such as multipliers and block memory. As these implementations exploit exclusively the fine-grain reconfigurable resources of Virtex FPGAs, they are easily portable to other FPGAs with similar reconfigurable fabrics without any major modifications. The pipelined designs of these two operations are evaluated in terms of area, throughput, and dynamic power consumption as a function of pipeline depth. Pipelining experiments reveal that the area overhead tends to remain constant regardless of the degree of pipelining to which the design is submitted, while the throughput increases with pipeline depth. In addition, these experiments reveal that pipelining reduces power considerably in shallow pipelines. Pipelining further these designs does not necessarily lead to significant power reduction. By partitioning these designs into deeper pipelines, these designs can reach throughputs close to the 100 MFLOPS mark by consuming a modest 1% to 8% of the reconfigurable fabric within a Virtex-II XC2VX000 (e.g., XC2V1000 or XC2V6000) FPGA

Series Expansion based Efficient Architectures for Double Precision Floating Point Division

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FPGA Implementation of Floating Point Reciprocator Using Binomial Expansion Method

Floating-point support has become a mandatory feature of new micro processors due to the prevalence of business, technical, and recreational applications that use these operations.  In these operations Floating-point division is generally regarded as a low frequency, high latency operation in typical floating-point applications. So due to this not much development had taken place in this field. But nowadays floating point divider has become indispensable and increasingly important in many scientific and signal processing applications.In this paper we implement floating point reciprocator for both single precision and double precision floating point numbers using FPGA. Here the implementation is based on the binomial expansion method. By comparing with previous works the modules occupy less area with a higher performance and less latency. The designs trade off either 1 unit in last-place (ulp) or 2 ulp of accuracy (for double or single precision respectively), without rounding, to obtain a better implementation

Performance and area evaluations of processor-based benchmarks on FPGA devices

The computing system on SoCs is being long-term research since the FPGA technology has emerged due to its personality of re-programmable fabric, reconfigurable computing, and fast development time to market. During the last decade, uni-processor in a SoC is no longer to deal with the high growing market for complex applications such as Mobile Phones audio and video encoding, image and network processing. Due to the number of transistors on a silicon wafer is increasing, the recent FPGAs or embedded systems are advancing toward multi-processor-based design to meet tremendous performance and benefit this kind of systems are possible. Therefore, is an upcoming age of the MPSoC. In addition, most of the embedded processors are soft-cores, because they are flexible and reconfigurable for specific software functions and easy to build homogenous multi-processor systems for parallel programming. Moreover, behavioural synthesis tools are becoming a lot more powerful and enable to create datapath of logic units from high-level algorithms such as C to HDL and available for partitioning a HW/SW concurrent methodology. A range of embedded processors is able to implement on a FPGA-based prototyping to integrate the CPUs on a programmable device. This research is, firstly represent different types of computer architectures in modern embedded processors that are followed in different type of software applications (eg. Multi-threading Operations or Complex Functions) on FPGA-based SoCs; and secondly investigate their capability by executing a wide-range of multimedia software codes (Integer-algometric only) in different models of the processor-systems (uni-processor or multi-processor or Co-design), and finally compare those results in terms of the benchmarks and resource utilizations within FPGAs. All the examined programs were written in standard C and executed in a variety numbers of soft-core processors or hardware units to obtain the execution times. However, the number of processors and their customizable configuration or hardware datapath being generated are limited by a target FPGA resource, and designers need to understand the FPGA-based tradeoffs that have been considered - Speed versus Area. For this experimental purpose, I defined benchmarks into DLP / HLS catalogues, which are "data" and "function" intensive respectively. The programs of DLP will be executed in LEON3 MP and LE1 CMP multi-processor systems and the programs of HLS in the LegUp Co-design system on target FPGAs. In preliminary, the performance of the soft-core processors will be examined by executing all the benchmarks. The whole story of this thesis work centres on the issue of the execute times or the speed-up and area breakdown on FPGA devices in terms of different programs

Floating Point Arithmetic for Transport Triggered Architectures

Laskentajärjestelmiin kohdistuu usein suorituskyky- ja virrankulutusvaatimuksia, joita ei pystytä saavuttamaan yleiskäyttöisellä prosessorilla. Toistaalta laitteistokiihdyttimien suunnittelu voi vaatia kohtuuttoman paljon työaikaa. Ongelmaa voidaan lähestyä käyttämällä sovellusta varten räätälöityä sovelluskohtaista käskykantaprosessoria (Application-Specific Instruction set Processor, ASIP), joka on kuitenkin ohjelmoitava. Prosessorin räätälöinnin täytyy olla pitkälle automatisoitua säästääkseen kustannuksia. TTA-based Codesign Environment (TCE) on siirtoliipaistuun prosessoriarkkitehtuuriin (Transport Triggered Architecture, TTA) perustuva ASIP-kehitysympäristö. TTA on arkkitehtuurina helposti räätälöitävä ja joustaa pienistä ytimistä suuritehoisiin pitkän käskysanan suorittimiin. Useat tieteellisen laskennan ja signaalinkäsittelyn sovellukset, joissa TTA:n skaalautuvuudesta ja käskytason rinnakkaisuudesta olisi erityistä hyötyä, vaativat tuen laitteistokiihdytetylle liukulukulaskennalle. Tässä diplomityössä suunniteltiin ja toteutettiin TCE-projektia varten sarja liukulukuyksiköitä. Yksiköiden suunnittelussa pyrittiin alustariippumattomuuteen sekä korkeaan suorituskykyyn Field Programmable Gate Array alustoilla (FPGA) jopa tinkimällä tuetusta liukulukustandardista. Yksiköt sisältävät työkalut puolen tarkkuuden liukulukulaskentaan. Lisäksi työssä esitetään erikoiskäskyihin perustuvat nopeat algoritmit liukulukujakolaskun ja -neliöjuuren laskentaan. Yksiköiden toiminta varmistettiin automaattisella rekisterisiirtotason (Register Transfer Level, RTL) testipenkillä. Vertailussa Altera Stratix-II-FPGA:lla yksiköt pääsivät lähelle Alteran omien liukulukuyksiköiden suorituskykyä. Uudemmalla Xilinx Virtex-6-FPGA:lla korkein mahdollinen suorituskyky vaatisi tiheämpää liukuhihnoitusta

Design of approximate overclocked datapath

Embedded applications can often demand stringent latency requirements. While high degrees of parallelism within custom FPGA-based accelerators may help to some extent, it may also be necessary to limit the precision used in the datapath to boost the operating frequency of the implementation. However, by reducing the precision, the engineer introduces quantisation error into the design. In this thesis, we describe an alternative circuit design methodology when considering trade-offs between accuracy, performance and silicon area. We compare two different approaches that could trade accuracy for performance. One is the traditional approach where the precision used in the datapath is limited to meet a target latency. The other is a proposed new approach which simply allows the datapath to operate without timing closure. We demonstrate analytically and experimentally that for many applications it would be preferable to simply overclock the design and accept that timing violations may arise. Since the errors introduced by timing violations occur rarely, they will cause less noise than quantisation errors. Furthermore, we show that conventional forms of computer arithmetic do not fail gracefully when pushed beyond the deterministic clocking region. In this thesis we take a fresh look at Online Arithmetic, originally proposed for digit serial operation, and synthesize unrolled digit parallel online arithmetic operators to allow for graceful degradation. We quantify the impact of timing violations on key arithmetic primitives, and show that substantial performance benefits can be obtained in comparison to binary arithmetic. Since timing errors are caused by long carry chains, these result in errors in least significant digits with online arithmetic, causing less impact than conventional implementations.Open Acces

Vector support for multicore processors with major emphasis on configurable multiprocessors

It recently became increasingly difficult to build higher speed uniprocessor chips because of performance degradation and high power consumption. The quadratically increasing circuit complexity forbade the exploration of more instruction-level parallelism (JLP). To continue raising the performance, processor designers then focused on thread-level parallelism (TLP) to realize a new architecture design paradigm. Multicore processor design is the result of this trend. It has proven quite capable in performance increase and provides new opportunities in power management and system scalability. But current multicore processors do not provide powerful vector architecture support which could yield significant speedups for array operations while maintaining arealpower efficiency. This dissertation proposes and presents the realization of an FPGA-based prototype of a multicore architecture with a shared vector unit (MCwSV). FPGA stands for Filed-Programmable Gate Array. The idea is that rather than improving only scalar or TLP performance, some hardware budget could be used to realize a vector unit to greatly speedup applications abundant in data-level parallelism (DLP). To be realistic, limited by the parallelism in the application itself and by the compiler\u27s vectorizing abilities, most of the general-purpose programs can only be partially vectorized. Thus, for efficient resource usage, one vector unit should be shared by several scalar processors. This approach could also keep the overall budget within acceptable limits. We suggest that this type of vector-unit sharing be established in future multicore chips. The design, implementation and evaluation of an MCwSV system with two scalar processors and a shared vector unit are presented for FPGA prototyping. The MicroBlaze processor, which is a commercial IP (Intellectual Property) core from Xilinx, is used as the scalar processor; in the experiments the vector unit is connected to a pair of MicroBlaze processors through standard bus interfaces. The overall system is organized in a decoupled and multi-banked structure. This organization provides substantial system scalability and better vector performance. For a given area budget, benchmarks from several areas show that the MCwSV system can provide significant performance increase as compared to a multicore system without a vector unit. However, a MCwSV system with two MicroBlazes and a shared vector unit is not always an optimized system configuration for various applications with different percentages of vectorization. On the other hand, the MCwSV framework was designed for easy scalability to potentially incorporate various numbers of scalar/vector units and various function units. Also, the flexibility inherent to FPGAs can aid the task of matching target applications. These benefits can be taken into account to create optimized MCwSV systems for various applications. So the work eventually focused on building an architecture design framework incorporating performance and resource management for application-specific MCwSV (AS-MCwSV) systems. For embedded system design, resource usage, power consumption and execution latency are three metrics to be used in design tradeoffs. The product of these metrics is used here to choose the MCwSV system with the smallest value

REAL-TIME ADAPTIVE PULSE COMPRESSION ON RECONFIGURABLE, SYSTEM-ON-CHIP (SOC) PLATFORMS

New radar applications need to perform complex algorithms and process a large quantity of data to generate useful information for the users. This situation has motivated the search for better processing solutions that include low-power high-performance processors, efficient algorithms, and high-speed interfaces. In this work, hardware implementation of adaptive pulse compression algorithms for real-time transceiver optimization is presented, and is based on a System-on-Chip architecture for reconfigurable hardware devices. This study also evaluates the performance of dedicated coprocessors as hardware accelerator units to speed up and improve the computation of computing-intensive tasks such matrix multiplication and matrix inversion, which are essential units to solve the covariance matrix. The tradeoffs between latency and hardware utilization are also presented. Moreover, the system architecture takes advantage of the embedded processor, which is interconnected with the logic resources through high-performance buses, to perform floating-point operations, control the processing blocks, and communicate with an external PC through a customized software interface. The overall system functionality is demonstrated and tested for real-time operations using a Ku-band testbed together with a low-cost channel emulator for different types of waveforms

Software/Hardware Tradeoffs in the Speedup of Color Image Processing Algorithms

Data parallel image processing algorithms have numerous uses in many real time applications. Depending on the complexity of the computations involved, these algorithms may take considerable amounts of time to complete. Since the algorithms are performed in real time, the end user is negatively impacted by the extended execution times. Fortunately, there are many different ways available in hardware and software to improve the speed of these algorithms. This thesis looks at several different methods of improving the speedup of color image processing algorithms and compares the tradeoffs among them. The methods for increasing the execution time of an algorithm include implementing Single Input Multiple Data (SIMD) instructions, using Posix threads to code across several processors, and using a stream based multichannel framework to implement the algorithms on an FPGA. Each of the above methods had advantages and disadvantages, yet all approaches were found to introduce a significant speedup over the single core baseline tests. These methods were completed on a number of different images to examine the effects of workload on the efficiency of the implementations. The application of these speedup techniques yielded excellent results leading to speedups of greater than 3.85 times in software and 5.8 times in hardware. In each of the software tests, the output image had a 2-d correlation coefficient (CORR2) of 1.0000. When implementing the algorithms in hardware using implementation specific approximations, the correlation coefficient of the output image was still an acceptable 0.99 or higher