RETIMING - Timing - page 242

which can be rewritten in terms of the phase shift operator as

In presence of skews at latches, the timing constraints in relation (7.17) and
(7.20), must be modified by using the latch shift operator instead of the phase
shift operator; only long path constraints are considered here. Thus, the timing
constraints for a level clocked circuit to be properly clocked by a clock schedule,
in presence of skews are

For simplicity, this discussion ignores the clock-to-Q delays and setup times,
though these may easily be inserted into these equations. These timing con-
straints can be rewritten as

To make the discussion simpler, we subtract from both sides of the first

relation, and substitute

The quantity is referred to as the Global Departure Time (GDT). Therefore,

we have

These can be rewritten as the following set of difference constraints:

The difference constraint between GDT values of two latches given in rela-
tion (10.29) is similar to the difference constraints between skews at FF's in
relation (10.8). This suggests a relation between retiming and GDT values of
level-sensitive latches, similar to the retiming-skew relationship for edge trig-
gered FF's. The following theorem is similar to the corresponding result for
edge-triggered circuits:
(a) Retiming transformations may be used to move latches from all of the
inputs of any combinational block to all of its outputs. The equivalent GDT of
the relocated latch at output considering long path constraints only, is given

by