Bitwise scheduling to balance the computational cost of behavioral specifications

Conventional scheduling algorithms try to balance the number of operations of every different type executed per cycle. However, in most cases, a uniform distribution is not reachable, and thus, some hardware (HW) waste appears. This situation becomes worse when heterogeneous specifications (those formed by operations with different data formats and widths) are synthesized. Our proposal is an innovative bit-level algorithm able to minimize this HW waste. In order to obtain uniform distributions of the computational cost of operations among cycles, it successively transforms specification operations into sets of smaller ones, which are then scheduled independently. As a consequence, some specification operations may be executed during a set of nonconsecutive cycles, and over several functional units. In combination with allocation algorithms able to guarantee the bit-level reuse of HW resources, our approach produces circuits with substantially smaller area than conventional implementations. Due to the fragmentation of operations, in the proposed implementations, the type, number, and width of HW resources are, in general, independent of the type, number, and width of both specification operations and variables. Additionally, the clock-cycle length is also reduced in most circuits.