Verification of Parameterised FPGA Circuit Descriptions with Layout ...

CHAPTER 3. GENERATING PARAMETERISED LIBRARIES WITH LAYOUT 62
function sum template(b : integer ; t : integer ) return integer is
constant b : integer := 0;
variable a : integer := 0;
variable n : integer ;
begin
for n in b to t loop
a := + a ;
end loop ;
return a ;
end function sum width ;
Figure 3.17: VHDL template for implementing the LE-Pebble sum function
Proof By induction on n and re-arrangement using established properties of maxf and sum.
Appendix B.9 gives mechanised proofs for these simplification rules.
Conditionals can sometimes be further simplified by taking advantage of the context specified
by assertions within blocks. For example, if a block contains an assertion which states m ≤ n
then the correct branch of an if expression dependent on that condition can be selected
statically. Alternatively, another common situation is for m = 0 and n ≥ 1 to be asserted,
which can also be used to simplify the same expression.
3.8 Compiling LE-Pebble into VHDL
To complete the process of generating parameterised hardware libraries in an industry-
standard format, LE-Pebble can be compiled into VHDL. The compilation of standard Pebble
into parameterised structural VHDL has been reported previously [46, 48] however the addi-
tion of new expression types that are not supported in VHDL to Pebble makes this process
slightly more complicated.
While VHDL does not support higher-order functions, it does support the definition of func-
tions within structural hardware descriptions. This mechanism can be used to compile com-
plex functions in LE-Pebble such as maxf into VHDL by generating functions based around
simple templates. Iterative version of sum and maxf are preferable for VHDL implemen-
tation and these can be described equivalent to the recursive definitions of these functions.
Figure 3.17 gives the VHDL template for the sum function. This can be instantiated for any
particular function by replacing the text “” with the expression to evaluate. This