Joint Optimization for Physical Synthesis

In other words, for a gate u driven by ii, i2, - -is the constraints to enforce A are shown below. Here I j S  

We subtract RAT(m) from the objective function since this variable is maximized rather than minimized. The AAT and RAT of registers (and other end points like primary input and output pins) are simply set according to initial values obtained form the reference timing model. The term —is added to the minimization objective. The total slack 2 can also easily be computed from the MILP and added as an objective. In practice, we minimize both. However, for brevity, we drop S from the MILP formulations for the remainder of the chapter. Note that the number of constraints in this formulation is proportional to the number of 2-pin arcs in the 

The min function is evaluated similarly. In Fig. 7.8, the slack, RAT, and AAT variables are real values while the retiming variables must be integer-valued. We utilize a constant weighting factor K to reconcile area with slack. The constant K can be adjusted based on the available area. 

Note that the formulation in Fig. 7.8 does not require the derivation of the W or D matrices that were described in Sect. 7.2. Instead, timing calculations are performed within the MILR Thus, the number of constraints is only 0 ( E ) for a retiming graph with edge set E. 

We first describe an LP formulation for local register relocation based on a simplified form of the LP in [10], We then incorporate it into our retiming formulation. 

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