Abstract: A method of assessing the stability of a placement tool used in designing the physical layout of an integrated circuit chip, by constructing different layouts of cells using the placement tool with different sets of input parameters, and calculating a stability value based on the movement of respective cell locations between the layouts. The stability value can be normalized based on cell locations in a random placement. One stability metric measures absolute movement of individual cells in the layouts, weighted by cell area. The cell movements can be squared in calculating the stability value. Another stability metric measures the relative movement of cells with respect to their nets. Shifting of cells and symmetric reversal of cells about a net center does not contribute to this relative movement, but spreading of cells and rotation of cells with respect to the net center does contribute to the relative movement. Relative cell movements can again be squared in calculating the stability value.

Abstract: A method of designing a layout of an integrated circuit first places logic cells in an initial region of the integrated circuit using a first placement algorithm then, after partitioning the initial region into two or more partitioned regions, uses a second placement algorithm (different from the first placement algorithm) to place a portion of the logic cells in at least one of the partitioned regions. The placement algorithms are preferably quadratic placement algorithms such as the conjugate gradient placement algorithm and the successive over-relaxation placement algorithm. The selection of the particular placement algorithm to be used may be based on, e.g., the cut level or the number moveable objects for the given partition region.

Abstract: A method and apparatus for determining routing feasibility of a plurality of nets. Each net has an associated set of one or more routing solutions, wherein each solution specifies one or more routing resources consumed by the net. A liveness Boolean function is generated having variables that represent respective net/solution pairs. If there exists a set of values for the variables such that at least one of the variables for each net is logically true, then the liveness function is true. An exclusivity function is generated using the variables that represent the net/solution pairs. If there exists at least one set of values for the variables such that no resource is used is by more than a predetermined number of nets, then the exclusivity function is true. The nets are routable using the provided solutions if there is one set of values for the variables such that both the liveness and exclusivity functions are true.

Abstract: A method of designing an integrated circuit including executing a placement algorithm to place a set of objects within the integrated circuit. The set of objects includes latched objects and non-latched objects. The algorithm places objects to minimize clock signal delay subject to a constraint on the placement distribution of the latched objects relative to the placement distribution of the non-latched objects. The latched object and non-latched object placement constraints may limit the difference between the latched object center of mass and a non-latched object center of mass. The latched object center of mass equals a sum of size-location products for each latched object divided by the sum of sizes for each latched object. The constraints may require that the latched object center of mass and the non-latched center of mass both equal the center of mass for all objects.

Abstract: A method of designing the layout of an integrated circuit (IC) by deriving an analytical constraint for a cut-based placement partitioner using analytical optimization, and placing cells on the IC with the cut-based placement partitioner using the analytical constraint. Quadratic optimization may be used to determine a desired ratio of a cell area of a given partition to a total cell area (the balance parameter), and placing may be performed using multilevel bisection partitioning constrained by the balance parameter. This implementation may include a determination of an aspect ratio for an entire partitioning region of the integrated circuit, and a “center-of-mass” coordinate of the cells based on the quadratic optimization, which are then used to define a placement rectangle having the same aspect ratio, and centered on the center-of-mass coordinate. This placement rectangle is used to derive the balance parameter.

Abstract: A method of designing the layout of an integrated circuit (IC) by deriving an analytical constraint for a cut-based placement partitioner using analytical optimization, and placing cells on the IC with the cut-based placement partitioner using the analytical constraint. Quadratic optimization may be used to determine a desired ratio of a cell area of a given partition to a total cell area (the balance parameter), and placing may be performed using multilevel bisection partitioning constrained by the balance parameter. This implementation may include a determination of an aspect ratio for an entire partitioning region of the integrated circuit, and a “center-of-mass” coordinate of the cells based on the quadratic optimization, which are then used to define a placement rectangle having the same aspect ratio, and centered on the center-of-mass coordinate. This placement rectangle is used to derive the balance parameter.