There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Due to its potential to greatly accelerate a wide variety of applications, reconfigurable computing has become a subject of a great deal of research. Its key feature is the ability to perform computations in hardware to increase performance, while retaining much of the flexibility of a software solution. In this survey, we explore the hardware aspects of reconfigurable computing machines, from single chip architectures to multi-chip systems, including internal structures and external coupling. We also focus on the software that targets these machines, such as compilation tools that map high-level algorithms directly to the reconfigurable substrate. Finally, we consider the issues involved in run-time reconfigurable systems, which reuse the configurable hardware during program execution.

/pdf/reconfigurable-computing-a-survey-of-systems-and-software-1bqra3qfdt.pdf

Reconfigurable computing: a survey of systems and software

International Technology Roadmap for Semiconductors 2003の要求清浄度について － シリコンウエハ表面と雰囲気環境に要求される清浄度, 分析方法の現状について －

Computational geometry

A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solve even large-scale GPs extremely efficiently and reliably; at the same time a number of practical problems, particularly in circuit design, have been found to be equivalent to (or well approximated by) GPs. Putting these two together, we get effective solutions for the practical problems. The basic approach in GP modeling is to attempt to express a practical problem, such as an engineering analysis or design problem, in GP format. In the best case, this formulation is exact; when this is not possible, we settle for an approximate formulation. This tutorial paper collects together in one place the basic background material needed to do GP modeling. We start with the basic definitions and facts, and some methods used to transform problems into GP format. We show how to recognize functions and problems compatible with GP, and how to approximate functions or data in a form compatible with GP (when this is possible). We give some simple and representative examples, and also describe some common extensions of GP, along with methods for solving (or approximately solving) them.

/pdf/a-tutorial-on-geometric-programming-47sdznbzxw.pdf

A tutorial on geometric programming

As the operation frequency reaches gigahertz in deep-submicron designs, the effects of inductance on noise and delay can no longer be neglected. Most of the previous works on inductance extraction are field-solvers, which are intrinsically more accurate but computationally expensive. Others focus on modeling the inductances of special routing topologies such as the bus structure. Therefore, it is not suitable to incorporate them on-line into a layout (placement and routing) tool for inductance (delay and noise) optimization. In this paper, we consider the overlapping of unequal wire lengths and dimensions to efficiently extract the loop inductance from the coplanar interconnect structure. The difference between our simulation results and the estimation values obtained by FastHenry l12r is within 10% for practical cases. In particular, our modeling is extremely efficient, and thus can be incorporated into a layout tool for inductance optimization.

https://ir.nctu.edu.tw:443/bitstream/11536/27999/1/000182319100007.pdf

Inductance Modeling for On-Chip Interconnects

Architecture and CAD are closely related issues in FPGA design. Routing architecture design shall optimize routability and facilitate router development; on the other hand, router design shall consider the specific properties of routing architectures to optimize the performance of the router. In this paper, we propose effective and efficient unified matching-based algorithms for array-based FPGA routing and segmentation design. For the segmentation design, we consider the similarity of input routing instances and formulate a net-matching problem to construct the optimal segmentation architecture. For the router design, we present a matching-based timing-driven routing algorithm which can consider a versatile set of routing segments. Experimental results show that our designed segmentations significantly outperform those used in commercially available FPGAs. For example, our designed segmentations achieve, on average, 14.6% and 19.7% improvements in routability, compared with those used in the Lucent Technologies ORCA 2C-series and the Xilinx XC4000E-series FPGAs, respectively.

/pdf/graph-matching-based-algorithms-for-array-based-fpga-3jpwxu8e15.pdf

Graph matching-based algorithms for array-based FPGA segmentation design and routing

As the technology advances, the pin number of a high-end PCB design keeps increasing. The staggered pin array is used to accommodate a larger pin number than the grid pin array of the same area. Nevertheless, escaping a large pin number to the boundary of a dense staggered pin array, namely multilayer escape routing for staggered pin arrays, is significantly harder than that for grid pin arrays. This paper addresses this multilayer escape routing problem to minimize the number of used layers in a staggered pin array for manufacturing cost reduction. We first present an escaped pin selection method to assign a maximal number of escaped pins in the current layer and also to increase useful routing regions for subsequent layers. Missing pins are also modeled in our routing network to utilize the routing resource effectively. Experimental results show that our approach can significantly reduce the required layer number for escape routing.

Layer minimization in escape routing for staggered-pin-array PCBs

In this paper, we present an X-architecture multilevel full-chip router, called X-Route. Unlike the traditional Λ-shaped multilevel framework that adopts bottom-up coarsening followed by top-down uncoarsening, our multilevel framework runs in the Vshaped manner: top-down uncoarsening followed by bottom-up coarsening. The top-down uncoarsening stage performs octagonal global routing and X-detailed routing for local nets at each level and then refines the solution for the next level. Then, the bottom-up coarsening stage performs the X-detailed routing to reroute failed nets and refines the solution level by level. Since we perform top-down routing first, global long nets are routed earlier. To prevent a wrong decision from blocking the later nets, we keep a dynamic congestion map that records the updated routing congestion information based on the routed nets and the global-path prediction of the unrouted nets. To take full advantage of the X-architecture, we also develop a progressive X-Steiner tree algorithm based on the delaunay triangulation approach for the X-architecture. Compared with the state-of-the-art Λ-shaped multilevel routing for the X-architecture, experimental results show that our X-Route reduces the respective wirelength and average delay by about 14.05% and 30.62%, with better routing completion.

X-Route: An X-architecture full-chip multilevel router

Due to the rapidly increasing design complexity in modern IC designs, metal-only engineering change order (ECO) becomes inevitable to achieve design closure with a low respin cost. Traditionally, preplaced redundant standard cells are regarded as spare cells. However, these cells are limited by predefined functionalities and locations, and they always consume leakage power despite their inputs are tied off. To overcome the inflexibility and power overhead, a new type of spare cells, metal-configurable gate-array spare cells, are considered. Therefore, in this paper, we address a new ECO problem: Timing ECO optimization using metal-configurable gate-array spare cells. We first study the properties for this new ECO problem, propose a new metric, aliveness, to model the capability of a spare gate array, and then develop a timing ECO optimization framework based on aliveness, routability, and timing satisfaction. Experimental results show that our approach delivers superior efficiency and effectiveness.

Yao-Wen Chang

Papers

Inductance Modeling for On-Chip Interconnects

Graph matching-based algorithms for array-based FPGA segmentation design and routing

Layer minimization in escape routing for staggered-pin-array PCBs

X-Route: An X-architecture full-chip multilevel router

Timing ECO optimization using metal-configurable gate-array spare cells