Reciprocal square root circuit design: a comparison of custom and automated design methodologies

The calculation of reciprocal square roots is vital to graphics rendering. This computation is performed often when rendering graphical images. The computation time required for a reciprocal square root calculation is high as a result of its complexity. A circuit dedicated to performing this floating point operation is proposed. The circuit is designed for implementation in a graphics ray tracing processor. Contemporary circuit designers have a wide variety of design tools and practices to select from when implementing a design. Continuous improvements in tools and techniques can lead to ambiguity when selecting which design methods to employ. The design of the reciprocal square root circuit is undertaken using both a custom and an automated circuit design flow. The results of this experiment are gathered and reviewed to determine costs and benefits of each method. The custom design flow utilizes an iterative architecture which demonstrates advantages of reduced gate count and circuit area by as much as 90%. The automated design flow utilizes a pipelined architecture that provides the advantages of greater throughput and shorter design time requirements by an order of magnitude. Both flows yield circuits of roughly comparable speed and latency. Some recommendations are provided for applying each technique to different types of applications. Applications such as embedded circuits may benefit from the custom design, where area and power consumption are critical. Applications requiring an abbreviated design flow or high throughput may be better suited to the automated flow.