architect: Arbitrary-precision Constant-hardware Iterative Compute

Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed or floating point, most of which operate least-significant digit first. This results in a fundamental problem: if, after some time, the result has not converged, is this because we have not run the algorithm for enough iterations or because the arithmetic in some iterations was insufficiently precise? There is no easy way to answer this question, so users will often over-budget precision in the hope that the answer will always be to run for a few more iterations. We propose a fundamentally new approach: armed with the appropriate arithmetic able to generate results from most-significant digit first, we show that fixed compute-area hardware can be used to calculate an arbitrary number of algorithmic iterations to arbitrary precision, with both precision and iteration index increasing in lockstep. Thus, datapaths constructed following our principles demonstrate efficiency over their traditional arithmetic equivalents where the latter’s precisions are either under- or over-budgeted for the computation of a result to a particular accuracy. For the execution of 100 iterations of the Jacobi method, we obtain a 1.60x increase in frequency and 15.7x LUT and 50.2x flip-flop reductions over a 2048-bit parallel-in, serial-out traditional arithmetic equivalent, along with 46.2x LUT and 83.3x flip-flop decreases versus the state-of-the-art online arithmetic implementation

FPGA structures for high speed and low overhead dynamic circuit specialization

A Field Programmable Gate Array (FPGA) is a programmable digital electronic chip. The FPGA does not come with a predefined function from the manufacturer; instead, the developer has to define its function through implementing a digital circuit on the FPGA resources. The functionality of the FPGA can be reprogrammed as desired and hence the name “field programmable”. FPGAs are useful in small volume digital electronic products as the design of a digital custom chip is expensive. Changing the FPGA (also called configuring it) is done by changing the configuration data (in the form of bitstreams) that defines the FPGA functionality. These bitstreams are stored in a memory of the FPGA called configuration memory. The SRAM cells of LookUp Tables (LUTs), Block Random Access Memories (BRAMs) and DSP blocks together form the configuration memory of an FPGA. The configuration data can be modified according to the user’s needs to implement the user-defined hardware. The simplest way to program the configuration memory is to download the bitstreams using a JTAG interface. However, modern techniques such as Partial Reconfiguration (PR) enable us to configure a part in the configuration memory with partial bitstreams during run-time. The reconfiguration is achieved by swapping in partial bitstreams into the configuration memory via a configuration interface called Internal Configuration Access Port (ICAP). The ICAP is a hardware primitive (macro) present in the FPGA used to access the configuration memory internally by an embedded processor. The reconfiguration technique adds flexibility to use specialized ci rcuits that are more compact and more efficient t han t heir b ulky c ounterparts. An example of such an implementation is the use of specialized multipliers instead of big generic multipliers in an FIR implementation with constant coefficients. To specialize these circuits and reconfigure during the run-time, researchers at the HES group proposed the novel technique called parameterized reconfiguration that can be used to efficiently and automatically implement Dynamic Circuit Specialization (DCS) that is built on top of the Partial Reconfiguration method. It uses the run-time reconfiguration technique that is tailored to implement a parameterized design. An application is said to be parameterized if some of its input values change much less frequently than the rest. These inputs are called parameters. Instead of implementing these parameters as regular inputs, in DCS these inputs are implemented as constants, and the application is optimized for the constants. For every change in parameter values, the design is re-optimized (specialized) during run-time and implemented by reconfiguring the optimized design for a new set of parameters. In DCS, the bitstreams of the parameterized design are expressed as Boolean functions of the parameters. For every infrequent change in parameters, a specialized FPGA configuration is generated by evaluating the corresponding Boolean functions, and the FPGA is reconfigured with the specialized configuration. A detailed study of overheads of DCS and providing suitable solutions with appropriate custom FPGA structures is the primary goal of the dissertation. I also suggest different improvements to the FPGA configuration memory architecture. After offering the custom FPGA structures, I investigated the role of DCS on FPGA overlays and the use of custom FPGA structures that help to reduce the overheads of DCS on FPGA overlays. By doing so, I hope I can convince the developer to use DCS (which now comes with minimal costs) in real-world applications. I start the investigations of overheads of DCS by implementing an adaptive FIR filter (using the DCS technique) on three different Xilinx FPGA platforms: Virtex-II Pro, Virtex-5, and Zynq-SoC. The study of how DCS behaves and what is its overhead in the evolution of the three FPGA platforms is the non-trivial basis to discover the costs of DCS. After that, I propose custom FPGA structures (reconfiguration controllers and reconfiguration drivers) to reduce the main overhead (reconfiguration time) of DCS. These structures not only reduce the reconfiguration time but also help curbing the power hungry part of the DCS system. After these chapters, I study the role of DCS on FPGA overlays. I investigate the effect of the proposed FPGA structures on Virtual-Coarse-Grained Reconfigurable Arrays (VCGRAs). I classify the VCGRA implementations into three types: the conventional VCGRA, partially parameterized VCGRA and fully parameterized VCGRA depending upon the level of parameterization. I have designed two variants of VCGRA grids for HPC image processing applications, namely, the MAC grid and Pixie. Finally, I try to tackle the reconfiguration time overhead at the hardware level of the FPGA by customizing the FPGA configuration memory architecture. In this part of my research, I propose to use a parallel memory structure to improve the reconfiguration time of DCS drastically. However, this improvement comes with a significant overhead of hardware resources which will need to be solved in future research on commercial FPGA configuration memory architectures