Verification of Parameterised FPGA Circuit Descriptions with Layout ...

APPENDIX D. CIRCUIT LAYOUT CASE STUDIES 270
/∗∗ Locater block determines which value of the state should be discarded.
@input bits Number of input bits
@input n Size of state array
@input a Value to look for
@input s State array to look in
@output d Array of true|false values to control the mode for the compactor
∗/
block locater (int bits) (int n) (‘t a, ‘t s[n+1]) ∼ (wire d[n+1]) {
wire found.
found = false.
((found, a), s) ;
row (n+1, lct cell bits) ;
pi1 ;
d at (0,0).
}
/∗∗ Compactor cell. Operates in shift or through mode. Shift means we
haven’t yet encountered the value to remove, through mode means we
have. In shift mode we push the current value to the left and output
the last value. In through mode we destroy the last value and output
this value directly , which will also be done by all subsequent nodes
∗/
block del cell (wire clk) (int bits) (‘t x, (‘t y, wire mode)) ∼ (‘t m, ‘t n) {
(y, x) ; mux bits mode ;n at (0,0).
(x, y) ; mux ff clk bits mode ;m at (1,0).
}
/∗∗ Compactor block takes a state of size n+1 and discards the specified
element to produce a new state of size n.
@input n Desired size of state array
@input s State array to look in
@input d Array of true|false values for whether this index is the value to
be removed
@output s2 Output state
∗/
block compactor (wire clk) (int bits) (int n) (‘t s[n+1], wire d[n+1]) ∼ (‘t s2[n]) {
(s [0], (s[n.. 1], d[n..1])) ;
[id, zip 2] ;
row (n, del cell clk bits) ;
pi1 ;
s2 at (0,0).
}
/∗∗ Take the median element ∗/
block midelem (int n) (‘t a[n]) ∼ (‘t b) {
assert (n mod 2 == 1) ”Can’t take the middle element of an even number!”.
b = a[n / 2].
}
/∗∗ Insert new value into block, then extract the median ∗/
block insert median (int bits) (int n) (‘t a, ‘t b[n]) ∼ (‘t c[n+1], ‘t d)
→ insert bits n ; fork ; snd (midelem (n+1)).
/∗∗ Remove element a from state s to produce state s2. Throw away d ∗/
block nextstate (wire clk) (int bits) (int n) (‘t a, ‘t s[n+1]) ∼ (‘t s2[n], bool d) {
wire control[n+1].
(a, s) ; locater bits n ; control at (0, height((s, control) ; compactor clk bits n ; s2)).