Verification of Parameterised FPGA Circuit Descriptions with Layout ...
Verification of Parameterised FPGA Circuit Descriptions with Layout ...
Verification of Parameterised FPGA Circuit Descriptions with Layout ...
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APPENDIX C. PLACED COMBINATOR LIBRARIES 261<br />
primrec<br />
"struct 0 R i o_ = (o_ = i)"<br />
"struct (Suc n) R i o_ = (let m = (2 pwr (int (Suc n))) in<br />
EX (st1_in::(’t20)vector) (st2_in::(’t20)vector) (st1_out::’t20) (st2_out::’t20).<br />
Def (i ;;; half $ (m div 2) ;;; (st1_in, st2_in)) &<br />
(if ((Suc n) mod 2) = 0 then (struct n R st1_in st1_out) & Def ((st1_out, st2_out<br />
) ;;; R ;;; o_) & (struct n R st2_in st2_out)<br />
else (struct n R st1_in st1_out) & Def ((st1_out, st2_out) ;;; R ;;; o_) & (<br />
struct n R st2_in st2_out)))"<br />
primrec<br />
"height 0 R i o_ = 0"<br />
"height (Suc n) R i o_ = (let m = (2 pwr (int (Suc n))) in<br />
let st1_in = (THE (st1_in::(’t20)vector). EX (st2_in::(’t20)vector) (st1_out::’<br />
t20) (st2_out::’t20).<br />
Def (i ;;; half $ (m div 2) ;;; (st1_in, st2_in)) &<br />
(if ((Suc n) mod 2) = 0 then (struct n R st1_in st1_out) & Def ((st1_out,<br />
st2_out) ;;; R ;;; o_) & (struct n R st2_in st2_out)<br />
else (struct n R st1_in st1_out) & Def ((st1_out, st2_out) ;;; R ;;; o_) & (<br />
struct n R st2_in st2_out))<br />
) in<br />
let st2_in = (THE (st2_in::(’t20)vector). EX (st1_in::(’t20)vector) (st1_out::’<br />
t20) (st2_out::’t20).<br />
Def (i ;;; half $ (m div 2) ;;; (st1_in, st2_in)) &<br />
(if ((Suc n) mod 2) = 0 then (struct n R st1_in st1_out) & Def ((st1_out,<br />
st2_out) ;;; R ;;; o_) & (struct n R st2_in st2_out)<br />
else (struct n R st1_in st1_out) & Def ((st1_out, st2_out) ;;; R ;;; o_) & (<br />
struct n R st2_in st2_out))<br />
) in<br />
let st1_out = (THE (st1_out::’t20). EX (st1_in::(’t20)vector) (st2_in::(’t20)<br />
vector) (st2_out::’t20).<br />
Def (i ;;; half $ (m div 2) ;;; (st1_in, st2_in)) &<br />
(if ((Suc n) mod 2) = 0 then (struct n R st1_in st1_out) & Def ((st1_out,<br />
st2_out) ;;; R ;;; o_) & (struct n R st2_in st2_out)<br />
else (struct n R st1_in st1_out) & Def ((st1_out, st2_out) ;;; R ;;; o_) & (<br />
struct n R st2_in st2_out))<br />
) in<br />
let st2_out = (THE (st2_out::’t20). EX (st1_in::(’t20)vector) (st2_in::(’t20)<br />
vector) (st1_out::’t20).<br />
Def (i ;;; half $ (m div 2) ;;; (st1_in, st2_in)) &<br />
(if ((Suc n) mod 2) = 0 then (struct n R st1_in st1_out) & Def ((st1_out,<br />
st2_out) ;;; R ;;; o_) & (struct n R st2_in st2_out)<br />
else (struct n R st1_in st1_out) & Def ((st1_out, st2_out) ;;; R ;;; o_) & (<br />
struct n R st2_in st2_out))<br />
) in<br />
max (Height (i ;;; half $ (m div 2) ;;; (st1_in, st2_in))) (if ((Suc n) mod 2) =<br />
0 then max ((height n R st1_in st1_out) + (Height ((st1_out, st2_out) ;;; R<br />
;;; o_)) + (height n R st2_in st2_out)) ((max ((height n R st1_in st1_out) +<br />
(Height ((st1_out, st2_out) ;;; R ;;; o_))) (height n R st1_in st1_out)))<br />
else max (height n R st2_in st2_out) ((max (Height ((st1_out, st2_out) ;;; R<br />
;;; o_)) (height n R st1_in st1_out))))<br />
)"<br />
primrec<br />
"width 0 R i o_ = 0"<br />
"width (Suc n) R i o_ = (let m = (2 pwr (int (Suc n))) in