Multi-terminal Nets do Change Conventional Wire Length Distribution Models

Conventional models for estimating wire lengths in computer chips use Rent's rule to estimate the number of terminals between sets of gates. The number of interconnections then follows by taking into account that most nets are pointto -point connections. In this paper, we introduce a model for multi-terminal nets and we show that such nets have a fundamentally different influence on the wire length estimations than point-to-point nets. The multi-terminal net model is then used to estimate the wire length distribution in two cases: (i) the distribution of source-sink pairs for applications of delay estimation and (ii) the distribution of Steiner tree lengths for applications related to routing resource estimation. The effects of including multi-terminal nets in the estimations are highlighted. Experiments show that the new estimated wire length distributions are close to the measured ones. Keywords Wire length estimation, Multi-terminal nets, Rent's rule. 1

Leading the Blind:Automated Transistor-Level Modeling for FPGA Architects

The design and development of innovative FPGA architectures hinge on the flexibility of its toolchain. Retargetable toolchains, like the Verilog-to-Routing (VTR) flow, have been developed to enable the testing of new FPGAs by mapping circuits onto easily-described and possibly theoretical architectures. However, in reality, the difficulty extends beyond having CAD tools that support the architectural changes: it is equally important for FPGA architects to be able to produce reliable delay and area models for these tools. In addition to having acute architectural intuitions, designing and optimizing the circuit at the transistor-level requires architects to have, as well, a particular set of electrical engineering skills and expertise. The process is also painstaking and time-consuming, rendering the comparison of a variety of architectures or the exploration of a wide design space quite complicated and even impossible in practice. In this work, we present a novel approach to model the delay and area of FPGA architectures with various structures and characteristics, quickly and with acceptable accuracy. Abstracting from the user the transistor-level design and optimization that normally accompany the model- ing process, this approach, called FPRESSO, can be used by any architect without prerequisites. We take inspiration from the way a standard-cell flow performs large-scale transistor-size optimization and apply the same concepts to FPGAs, only at a coarser granularity. Skilled designers prepare for FPRESSO a set of locally optimized libraries of basic parameterizable components with a variety of drive strengths. Then, inexperienced users specify arbitrary FPGA architectures as interconnects of these basic components. The architecture is globally optimized, within minutes, through a standard logic synthesis tool, by choosing the most fitting version of each cell and adding buffers wherever appropriate. The resulting delay and area characteristics are automatically returned, in a format suitable for the VTR flow. A correct modeling of any architecture requires not only an optimization of the logic components, but also a proper modeling of the wires connecting these components. This does not only include measuring the length of the wires to determine their respective resistance and capacitance, but also, minimizing their length to reduce the wireload effect on the overall performance. To that end, FPRESSO features an automatic and generic wire modeling approach based on a simulated annealing floorplanning algorithm, to estimate the wires between the different components of the FPGA architecture. To evaluate the results of FPRESSO and confirm the validity of its modeled architectures, we use it to explore a wide range of FPGA architectures. First, we repeat a known study that helped set the standards on the optimal Look-Up-Table (LUT) and cluster size for conventional FPGAs. We show, by comparing with the results of the study, that modeling in FPRESSO preserves the very same trends and conclusions, with significantly less effort. We then extend the search space to cover fracturable LUTs and sparse crossbars, and show how FPRESSO makes the exploration of a huge search space not only possible but easy, efficient, and affordable, for any class of VTR users