Verification of Parameterised FPGA Circuit Descriptions with Layout ...

CHAPTER 3. GENERATING PARAMETERISED LIBRARIES WITH LAYOUT 52
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(a) Default layout interpretation
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(b) A better layout interpretation
Figure 3.13: A grid of m ×n A elements surrounded by B and C elements can have multiple
layout interpretations. Shown here for n = 4, m = 6.
3.6.1 Composition
Series and parallel composition have been given particular layout interpretations. This means
that a series composition will always place elements from left to right, and a parallel compo-
sition will always stack elements vertically. In this case, we want the parallel composition to
be “wrapped around” the top and bottom of the grid - not something that can be achieved
within the current framework since it implies that the grid is placed within the bounding box
described by the parallel compositions. There are, however, three solutions that can resolve
this situation:
1. The Quartz description can be re-cast using the beside and below combinators. This
would be quite effective, however it introduces some unnecessary complexity since beside
and below operate on blocks with four connections and the map n B and map m C blocks
have only two. The π1 −1 /π1 and π2 −1 /π2 wiring blocks can be used to resolve this
issue, however the resulting description will be less clear than the original.
2. The series and parallel compositions can be expanded out into separate block instan-
tiations with explicit internal signals. This new expanded version can be derived from
the original description by refinement. After the new description has been produced,
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