Verification of Parameterised FPGA Circuit Descriptions with Layout ...

CHAPTER 5. SPECIALISATION 112
// Hardware primitive
block xor2 (wire a, wire b) ∼ (wire c) attributes { height = 1. width = 1. }{ }
// Specialising when both inputs are known
block xor2 (bool a, bool b) ∼ (bool c) attributes { width = 0. height = 0. }
→ c = (a xor b).
// Specialising when one input is known
block xor2 (bool a, wire b) ∼ (wire c)
attributes { width = if (a,1,0). height = if (a,1,0). }
→ if a { b ; inv ; c. } else { c = b. } .
block xor2 (wire a, bool b) ∼ (wire c)
→ (b, a) ; xor2 ; c.
5.2.2 Benefits
Figure 5.4: Distributed specialisation of an xor2 block
So far we have given simple examples of how distributed specialisation can be used to achieve
constant propagation and elimination of unnecessary logic primitives. It is worth pointing
out that this operation will be carried out by any reasonable synthesis tool anyway and we are
not claiming that applying constant propagation to circuits is anything new. The strengths
of distributed specialisation are its three advantages over low-level hardware optimisation by
synthesis tools.
Firstly, when using components that implement distributed specialisation in a laid out circuit,
the circuit placement can itself be parameterised by the static parameters. This means that
blocks can shrink in size as logic is eliminated and the remainder of the circuit components’
positions will be adjusted accordingly. Low-level constant propagation can not achieve this,
even if operating only on a placed rather than placed & routed circuit. While the synthesis
tools will eliminate logic that is not being used, it does not change the positions of other
elements of the circuit and could not know how to move them anyway since the circuit layout
is only parameterised in the high-level description. By moving specialisation up to the same
level as the layout description (the HDL level) we are able to make sure that the layout is
parameterised and not only propagate constants through a design but also achieve design
compaction.
Compaction has two advantages. It allows specialisation to reduce the overall size of the