This paper presents a formal design of arithmetic circuits using an arithmetic description language called ARITH. The key idea in ARITH is to describe arithmetic algorithms directly with high-level mathematical objects (i.e., number representation systems and arithmetic operations/formulae). Using ARITH, we can provide formal description of arithmetic algorithms including those using unconventional number systems. In addition, the described arithmetic algorithms can be formally verified by equivalence checking with formula manipulations. The verified ARITH descriptions are easily translated into the equivalent HDL descriptions. In this paper, we also present an application of ARITH to an arithmetic module generator, which supports a variety of hardware algorithms for 2-operand adders, multi-operand adders, multipliers, constant-coefficient multipliers and multiply accumulators. The language processing system of ARITH incorporated in the generator verifies the correctness of ARITH descriptions in a formal method. As a result, we can obtain highly-reliable arithmetic modules whose functions are completely verified at the algorithm level.

This paper describes the design and development of a module generator for a dual-rail PLA with embedded 2-input logic cells for 0.35 µm CMOS technology. In order to automatically generate logic-cell based PLA layouts from circuit specifications, a module generator as a design automation tool of logic-cell based PLA is developed with a structural improvement. This module generator is based on a timing-driven design methodology and consists of logic synthesis, transistor sizing and logic cell generation, stimulus generation, HDL model generation parts. This generator uses a design constraint to achieve a flexible transistor sizing in a logic cell generation part. In addition, generated logic cells can be easily adapted to a layout generator. The layout is generated by using 0.35 µm, 3-metal-layer CMOS technology. Moreover, an HDL model generator is developed to create delay behavior models easily and quickly with precise timing parameters. The design complexity which is becoming an important issue for VLSI circuits can be reduced partially and human caused errors are minimized by module generator. A PLA layout in GDS-II form and an HDL model behavior of a Boolean function which has 64-bit input, 1-bit output and 220 product term can be generated within 8 minutes on a SunUltraSPARC-III 900 MHz processor. A very short time is required to compile the module, and this makes it feasible for designers to try many different design configurations in order to get the better one.

We propose a new multiple folding algorithm for the gate matrix layout, and apply it to generation of rectangular blocks with flexible size. The algorithm consists of two phases, the net partitioning and the gate arangement, and both algorithms are based on the multi-way mini-cut technique. In the first and second phases, the width and height of the multiple folded gate matrix block are directly minimized, resperctively, such that the area is minimized and desired aspect ratio of the block is obtained. The features of the present algorithm are as hollows: (1) Dead space on the gate matrix block can be minimized, (2) the aspect ratio can be controlled finely, (3) since polar graphs are successfully used in the second phase, the efficiency of the algorithm can be much improved. The experimental results show the effectiveness of our algorithm.

A new applicative design language is proposed for developing generators of data-path modules from hardware algorithms. The language includes a set of primitives that represent placement operations, parameterized cells, routing patterns and a set of transformation rules specifying modifications of the module topology without changing its functionality. Using the language, a hardware algorithm designer can easily define both the topological and geometrical specifications of module generation directly at the functional level without engaged in the layout details. A sketch of the language and an example of module design with the language is presented.