Verification of Parameterised FPGA Circuit Descriptions with Layout ...

CHAPTER 5. SPECIALISATION 110
A B Q
0 0 0
0 1 0
1 0 0
1 1 1
(a) 2-input
B Q
0 0
1 1
(b) A=true
B Q
0 0
1 0
(c) A=false
Figure 5.1: AND gate truth tables
about them, we instead totally replace them with Quartz variables.
5.2.1 Specialising Primitives
We will first introduce this simple but powerful idea with a basic example: a 2-input logical
and gate. The truth table for a 2-input and gate is shown in Figure 5.1(a), showing that
the output signal Q is only asserted if both the inputs A and B are true. If one of the
input signals is known then this truth table can be simplified as shown in Figure 5.1(b) and
Figure 5.1(c). If A is false, then Q always equals false, regardless of the value of B, while if
A is true then Q takes the value of B.
This allows us to describe the specialisation of an and gate when the A input is fixed - if it
is fixed with value true then the gate should specialise to a wire linking Q and B, while if it
fixed with value false then Q should just be statically assigned the value false.
In distributed specialisation we enclose this behaviour within a composite and2 block which
will transparently carry out this operation when connected to a static value. We can use
the Quartz overloading mechanism to select between different possible uses of the and gate
primitive - with two wire values, or one wire and one known value or two known values - using
the type system, assuming that static values are represented as Quartz booleans. Figure 5.2
illustrates the overloaded Quartz blocks that can describe this operation.
If the two input values are unknown (i.e. they are real dynamic values carried on hardware
wires) then the hardware primitive and2 is selected which elaborates to a primitive gate with
size 1 × 1. If both inputs are known then no hardware is generated at all and instead a
boolean output variable is generated with the value of the and operation. If one input is
known then either a wire or a static assignment of c to ground is generated.