Abstract: In a computer implemented method, possible arrangements of items, such as components to be placed on a semiconductor die, are described in a permutation space expressed as a data structure stored in a memory. The data structure is in the form of a balanced tree. In the tree, each node is a possible permutation. The ordering in the permutation space is transformed to an ordering described in a vector space using an inversion table. A best ordering of items is determined in the vector space according to a predetermined criterion such as an objective function. The best ordering as determined in vector space is then transformed back to the permutation space to determine an optimal placement of the item according to the predetermined criterion.

Abstract: System and method for reducing the processing time or latency of floating point arithmetic operations by eliminating the need to complement a negative result produced by a subtraction operation. Each of two numbers is subtracted from the other in simultaneous parallel subtraction operations to produce one answer which is positive and one answer which is negative. The answer which is positive is selected as the result of the operation.