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Folding, Retiming & Recoding Continued

Flip-flop migration can affect critical paths:

  a <= b + c;            b1 <=c; c1 <= c;        
  q <= (d) ? a:0;        q <= (d) ? b1+c1:0;

Alternatively, pushing the multiplexor back will require an earlier version of d that might not be available (e.g. if it were an external input).

Problems arising:

Circuits containing loops (proper synchronous loops) cannot be pushed with a simple algorithm since the algorithm loops.
External interfaces that do not use transactional handshakes (i.e. those without flow control) cannot tolerate automatic re-timing since the knowledge about when data is valid is not explicit.

but retiming can overcome structural hazards (e.g. the 'write back' cycle in RISC pipeline).

Other rewrites commonly use: automatically introduce one-hot and gray encoding, or invert for reset as preset.