Using symbolic computer algebra for subexpression factorization and subexpression decomposition in high level synthesis

In high level synthesis, signals can usually be regarded as symbols. With modern symbolic computer algebra, behavioral-level circuit descriptions consisting of symbols can be transformed into more efficient codes for hardware implementation. In this paper, two high level transformation techniques, subexpression factorization and subexpression decomposition, which are based on modern symbolic computer algebra, are proposed to optimize both area and critical path delay (CPD). The subexpression factorization tries to find an optimal combination of subexpressions of the input polynomial for hardware implementation. The subexpression decomposition tries to achieve the best decomposition of a polynomial for the mapping of complex components.