Integer arithmetic method for wire length minimization in global placement with convolution based density penalty computation

Abstract

A putative circuit design is represented as a set of movable blocks of predetermined size which must fit into a bounding box, with a plurality of subsets to be interconnected by wires. A total weighted wire length is determined as a function of coordinates of centers of the movable blocks by summing a half perimeter wire length over the plurality of subsets, and a density penalty is determined as a convolution of an indicator function of the current placement and a convolution kernel, via incremental integer computation without use of floating point arithmetic. Blocks are moved to minimize a penalty function which is the sum of the total weighted wire length and the product of a density penalty weight and the density penalty. The process repeats until a maximum value of the density penalty weight is reached or the density penalty approaches zero.