Vrije Universiteit Brussel Faculteit van de Wetenschappen Vakgroep Informatica. Deel 2a: Ontwerp van register machines

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1 Vrije Universiteit Brussel Faculteit van de Wetenschappen Vakgroep Informatica Deel 2a: Ontwerp van registermachines Interpretatie van Computerprogramma's I Theo D'Hondt p. 1

2 Register Machines registers data paths operaties = controller sekwentie p. 2

3 Voorbeeld registers het algoritme van Euclides voor de grootste gemene deler van twee natuurlijke getallen (define (gcd a b) (if (= b 0) a (gcd (b (remainder a b)))) sekwentie operaties p. 3

4 Data-path diagram a a<-b b = rem b<-t t<-r t 0 p. 4

5 Betekenis t register t<-r toekenning rem operatie sekwentie = predicaat 0 constante p. 5

6 Controller diagram start = nee ja stop t<-r a<-b b<-t p. 6

7 Gebruik van een specificatietaal (data-paths (registers ((name a) (buttons ((name a<-b) (source (register b))))) ((name b) (buttons ((name b<-t) (source (register t))))) ((name t) (buttons ((name t<-r) (source (operation rem)))))) (operations ((name rem) (inputs (register a) (register b))) ((name =) (inputs (register b) (constant 0))))) (controller test-b ; label (test =) ; test (branch (label gcd-done)) ; conditional branch (t<-r) ; button-push (a<-b) ; button-push (b<-t) ; button-push (goto (label test-b)) ; unconditional branch gcd-done) ; label p. 7

8 Formele beschrijving van een machine (controller <instructions>) GCD (controller test-b (test (op =) (reg b) (const 0)) (branch (label gcd-done)) (assign t (op rem) (reg a) (reg b)) (assign a (reg b)) (assign b (reg t)) (goto (label test-b)) gcd-done) p. 8

9 GCD-machine die leest en schrijft read a<-rd b<-rd a a<-b b = P print rem b<-t t<-r t 0 p. 9

10 Specificatie GCD (controller gcd-loop (assign a (op read)) (assign b (op read)) test-b (test (op =) (reg b) (const 0)) (branch (label gcd-done)) (assign t (op rem) (reg a) (reg b)) (assign a (reg b)) (assign b (reg t)) (goto (label test-b)) gcd-done (perform (op print) (reg a)) (goto (label gcd-loop))) p. 10

11 Uitgewerkte GCD-machine (define (remainder n d) (if (n < d) n (remainder (- n d) d))) p. 11

12 Uitgewerkte GCD-machine: data-paths a<-b a b = t<-a b<-t t < t<-d rem 0 p. 12

13 Uitgewerkte GCD-machine: controller start = ja stop t<-a nee t<-a < nee a<-b ja b<-t p. 13

14 Uitgewerkte GCD-machine: specificatie (controller test-b (test (op =) (reg b) (const 0)) (branch (label gcd-done)) (assign t (reg a)) rem-loop (test (op <) (reg t) (reg b)) (branch (label rem-done)) (assign t (op -) (reg t) (reg b)) (goto (label rem-loop)) rem-done (assign a (reg b)) (assign b (reg t)) (goto (label test-b)) gcd-done) GCD p. 14

15 Subroutines: het 2 x gcd voorbeeld a a<-b b = c c<-d d = rem b<-t t<-r rem d<-s t 0 s<-r s 0 p. 15

16 Volledig ontdubbelde specificaties (controller... gcd-1 (test (op =) (reg b) (const 0)) (branch (label after-gcd-1)) (assign t (op rem) (reg a) (reg b)) (assign a (reg b)) (assign b (reg t)) (goto (label gcd-1)) after-gcd-1... gcd-2 (test (op =) (reg d) (const 0)) (branch (label after-gcd-2)) (assign s (op rem) (reg c) (reg d)) (assign c (reg d)) (assign d (reg s)) (goto (label gcd-1)) after-gcd-2... ) p. 16

17 Gemeenschappelijke data-paths (controller... gcd-1 (test (op =) (reg b) (const 0)) (branch (label after-gcd-1)) (assign t (op rem) (reg a) (reg b)) (assign a (reg b)) (assign b (reg t)) (goto (label gcd-1)) after-gcd-1... gcd-2 (test (op =) (reg b) (const 0)) (branch (label after-gcd-2)) (assign t (op rem) (reg a) (reg b)) (assign a (reg b)) (assign b (reg t)) (goto (label gcd-2)) after-gcd-2... ) p. 17

18 Gemeenschappelijke controller gcd (test (op =) (reg b) (const 0)) (branch (label gcd-done)) (assign t (op rem) (reg a) (reg b)) (assign a (reg b)) (assign b (reg t)) (goto (label gcd)) gcd-done (test (op =) (reg continue) (const 0)) (branch (label gcd-1-done)) (goto (label gcd-2-done))... gcd-1 (assign continue 0) (goto gcd) gcd-1-done... gcd-2 (assign continue 1) (goto gcd) gcd-2-done...) p. 18

19 Labels als waarde gcd (test (op =) (reg b) (const 0)) (branch (label gcd-done)) (assign t (op rem) (reg a) (reg b)) (assign a (reg b)) (assign b (reg t)) (goto (label gcd)) gcd-done (goto (reg continue))... gcd-1 (assign continue gcd-1-done) (goto gcd) gcd-1-done... gcd-2 (assign continue gcd-2-done) (goto gcd) gcd-2-done...) p. 19

20 Recursieve processen (define (fac n) (if (= n 1) 1 (* (fac (- n 1)) n))) p. 20

21 Recursie via een stapel = val 1 n rn sn stack * - controller sc rc continue stack after-fact fact-done p. 21

22 Recursie via een stapel (controller (assign continue (label fact-done)) fact-loop (test (op =) (reg n) (const 1)) (branch (label base-case)) (save continue) (save n) (assign n (op -) (reg n) (const 1)) (assign continue (label after-fact)) (goto (label fact-loop)) after-fact (restore n) (restore continue) (assign val (op *) (reg n) (reg val)) (goto (reg continue)) base-case (assign val (const 1)) (goto (reg continue)) return to caller fact-done) factorial-machine p. 22

23 Complexe recursieve processen (define (fib n) (if (< n 2) n (+ (fib (- n 1)) (fib (- n 2))))) p. 23

24 Het Fibonacci controle-programma (controller (assign continue (label fib-done)) fib-loop (test (op <) (reg n) (const 2)) (branch (label immediate-answer)) (save continue) (assign continue (label afterfib-n-1)) (save n) (assign n (op -) (reg n) (const 1)) (goto (label fib-loop)) afterfib-n-1 (restore n) (restore continue) (assign n (op -) (reg n) (const 2)) (save continue) (assign continue (label afterfib-n-2)) (save val) (goto (label fib-loop)) p. 24

25 Het Fibonacci controle-programma afterfib-n-2 (assign n (reg val)) (restore val) (restore continue) (assign val (op +) (reg val) (reg n)) (goto (reg continue)) immediate-answer (assign val (reg n)) (goto (reg continue)) fib-done) p. 25