Search

We consider the problem of choosing the gate sizes or scale factors in a combinational logic circuit in order to minimize the total area, subject to simple RC timing constraints, and a minimum-allowed gate size. This problem is well known to be a geometric program (GP), and can be solved by using standard interior-point methods for small- and medium-size problems with up to several thousand gates. In this paper, we describe a new method for solving this problem that handles far larger circuits, up to a million gates, and is far faster. Numerical experiments show that our method can compute an adequately accurate solution within around 200 iterations; each iteration, in turn, consists of a few passes over the circuit. In particular, the complexity of our method, with a fixed number of iterations, is linear in the number of gates. A simple implementation of our algorithm can size a 10000 gate circuit in 25 s, a 100 000 gate circuit in 4 mm, and a million gate circuit in 40 mm, approximately. For the million gate circuit, the associated GP has three million variables and more than six million monomial terms in its constraints; as far as we know, these are the largest GPs ever solved. [ABSTRACT FROM AUTHOR]

In this paper, the main features and performances of a new numerical scheme, ILILPM (Improved Locally and Instantaneously Linearized Parabolic Model) are described. ILILPM is an improved version of the Parabolic and Backwater (PAB) and Linearized Parabolic Model (LPM) schemes, proposed in literature for the approximate solution of the Parabolic Wave model. The algorithm presented is able to take into account transcritical flow regime and transitions from free-surface to pressurized flow in tree-like channel networks. Due to its unconditional stability, the model allows large computational time steps, leading to very fast simulations during transients for a class of flow conditions larger than those solved by the parent schemes. The model is demonstrated by comparing its results with experimental observations and with the results provided by the numerical solution of the full De Saint-Venant equations. [ABSTRACT FROM AUTHOR]