An exact algorithm for the maximal sharing of partial terms in multiple constant multiplications

— In this paper we propose an exact algorithm that maximizes the sharing of partial terms in Multiple Constant Multiplication (MCM) operations. We model this problem as a Boolean network that covers all possible partial terms which may be used to generate the set of coefficients in the MCM instance. The PIs to this network are shifted versions of the MCM input. An AND gate represents an adder or a subtracter, i.e., an AND gate generates a new partial term. All partial terms that have the same numerical value are ORed together. There is a single output which is an AND over all the coefficients in the MCM. We cast this problem into a 0-1 Integer Linear Programming (ILP) problem by requiring that the output is asserted while minimizing the total number of AND gates that evaluate to one. A SAT-based solver is used to obtain the exact solution. We argue that for many real problems the size of the problem is within the capabilities of current SAT solvers. We present results using binary,...

• Type: Conference
• Year: 2005
• Where: ICCAD
• Authors: Paulo F. Flores, José C. Monteiro, Eduardo A. C. da Costa
• Keywords: Hardware, ICCAD 2005, MCM Instance, Partial Terms, Possible Partial Terms