Minimum area retiming with equivalent initial states

Abstract

Traditional minimum area retiming algorithms attempt to achieve their prescribed objective with no regard to maintaining the initial state of the system. This issue is important for circuits such as controllers, and our work addresses this problem. The procedure described generates bounds on the retiming variables that guarantee an equivalent initial state after retiming. A number of possible sets of bounds can be derived, and each set is used to solve a minimum area retiming problem that is set up as a 0/1 mixed integer linear program, using a new technique that models the maximal sharing of flip-flops at latch outputs. The best solution is found through enumeration of these sets, terminated on achievement of a calculated lower bound. Experimental results show that after a small number of enumerations, optimal or near-optimal results are achievable.

Scalable min-register retiming under timing and initializability constraints

“…In [16] a heuristic transformation is introduced for altering any minimum-delay retiming. For the minimum-register problem, [10] describes a solution, but it requires the formulation of retiming as a mixed-integer linear program (MILP), making it only useful for small circuits.…”

“…If no equivalent initial state is found to exist, either the retiming must be restricted to the forward direction to ensure feasibility [8] or additional combinational logic synthesized [17]. The solution proposed by [10] does not scale beyond small designs. Minimally transforming a useful retiming without an equivalent initial state into one that has an equivalent initial state is a difficult problem.…”

A practical approach to multiple-class retiming

“…Although this may result in maximal backward retiming bounds which can actually not be achieved due to justification conflicts, we decided to ignore reset values for two reasons. First, it was shown in [13] that retiming constraints which guarantee justifiable reset values are generally not unique resulting in a large number of different constraint sets. Thus, in order to find the optimal solution a retiming must be computed for each constraint set.…”

“…Recently, Maheshwari and Sapatnekar proposed an extended register sharing model [13] which takes into account restricted sharing due to different reset values. Their model could also be adapted to work with multiple-class retiming.…”

“…Efficient implementations [16,12,11] have made retiming applicable to large circuits. Important contributions have been made to apply retiming to circuits with reset states [19,4,18,13]. Finally, it has been shown that retiming can be used together with existing combinational optimization techniques [14,2,3,15,5], to further improve circuit performance.…”