Verification of Parameterised FPGA Circuit Descriptions with Layout ...

CHAPTER 3. GENERATING PARAMETERISED LIBRARIES WITH LAYOUT 51
rippleadd is not a combinator and thus much simpler height and width expressions have been
specified than would be inferred by the inference algorithm (though the result is the same).
The zip and apr blocks are both pure wiring which require zero room so the row of full adders
is the only block which actually contributes to the size of rippleadd - and since fadd has a
constant height and width the size of the whole ripple adder can be described extremely
clearly.
Figure 3.12 shows the layout of the ripple adder circuit for n = 4.
3.6 Different Layout Interpretations
While functional descriptions of Quartz designs tend to have a useful obvious layout inter-
pretation, it is often the case that designs have more than one possible layout interpretation.
For example, the ripple adder illustrated as a row in Figure 3.12 could equally be described
as a vertical array of full-adders. In this case we could use the col combinator rather than
the row combinator however because Quartz combinators describe both function and layout
it is sometimes desirable to use the same combinator with a different layout interpretation.
For example, an m×n grid of A elements, surrounded by interface elements B on the domain
and C on the range can be described in Quartz as:
[map n B, map m B] ; grid m,n A ; [map m C, map n C]
This is a common circuit structure, for example where blocks B and C could be input and
output registers. However, the standard layout interpretation attached to Quartz constructs
will produce the layout shown in Figure 3.13(a). This is not the worst possible layout that
could be assigned to this circuit but it is far from compact with long wire lengths and a large
area of unused logic resources.
A better layout interpretation would be that shown in Figure 3.13(b). This layout can be
enclosed in a much smaller bounding box and has shorter wires between the B and C elements
and the grid. However, this layout is difficult to generate with the system as described so
far.