Verification of Parameterised FPGA Circuit Descriptions with Layout ...

CHAPTER 3. GENERATING PARAMETERISED LIBRARIES WITH LAYOUT 46
block beside (block R (‘a, ‘b) ∼ (‘d, ‘x), block S (‘x, ‘c) ∼ (‘e, ‘f))
(‘a a, (‘b b, ‘c c)) ∼ ((‘d d, ‘e e), ‘f f)
attributes {
width = width((a,b) ;R ;(d, is )) + width((is, c) ; S ; (e, f)).
height = max (height ((a, b) ;R ;(d, is )), height((is, c) ; S ; (e, f))).
}
{
‘x is.
(a, b) ; R ; (d, is) at (0,0).
(is , c) ; S ; (e, f) at (width((a, b) ; R ; (d, is )), 0).
}
Figure 3.7: A placed interpretation of the Quartz beside combinator
non-optimal) static approximation to this value.
The function is defined recursively over the structure of statements, with three basic cases.
Assignments and assertions are given size expressions (0,0) since they are assumed to take
up no space. Block instantiations have size expressions that are the size of the instantiation
itself added to its x and y placed position. Conditional generation statements produce a
conditional expression. Iteration statements are the most interesting construct, here the
maxf function is used to select the maximum size values as the loop variable varies between
its lower and upper limit. If the loop upper bound is less than its lower bound (e2 < e1 in
Figure 3.6) then the loop never executes and this is reflected in the semantics for maxf which
returns zero in these circumstances.
3.5 Parameterised Quartz with Placement
These concepts can be brought together to write Quartz code with relative placement using
explicit co-ordinates.
3.5.1 Laid-out Combinators
In Figure 3.7 a version of the R↔S (beside) combinator which has been laid out with relative
positioning is illustrated. The block R is placed at the origin and the block S is beside it
with a y-offset of zero and an x-offset of the width of the R block.