Compiling Communicating Processes into Delay-Insensitive VLSI Circuits

1. Compiling Communicating Processes into Delay-Insensitive VLSI Circuits Alain J. Martin Department of Computer Science California Institute of Technology

2. Communicating Hardware Processes • Inspired by: • Hoare's communicating sequential processes • (CSP). • Dijkstra's guarded commands. • Based on: • Concurrent processes communicating by • message­passing.

3. Communicating Hardware Processes • Data Types • Only basic type is the boolean. • Other types are collections of booleans • represented using PASCAL record notation. • Example:alu = record • op : alu.15..alu.12 • x : alu.11..alu.8 • y : alu.7..alu.4 • z : alu.3..alu.0 • end • 8-bit integer x : x.0, x.1, ..., x.7.

4. Communicating Hardware Processes • Assignment: • For a boolean b: • The command b:=true • assigns the value true to b • (also denoted b+ or ). • The command b:=false • assigns the value false to b • (also denoted b- or ). • Given two integers x and y of the same length n: • y := x ==> y.0, y.1, ..., y.(n-1) := x.0, x.1, ..., x.(n-1). b b

5. Communicating Hardware Processes • Arrays: • Arrays are used when the identity of the element • in a set of variables that is to be used for some • action is determined during the computation. • Example: • reg[i.z] := aluf (reg[i.x], reg[i.y], i.op) • Note: instruction i is of of type alu

6. Communicating Hardware Processes • Composition Operators • There are three composition operators: • The sequential operator: ;. • The concurrent, or parallel, operator: ||. • The coincident, or bullet, operator: ..

7. Communicating Hardware Processes • Sequential Operator • S 1;S 2 means first execute S 1 then execute S 2 . • The ``;'' operator is associative: • (S 1 ; S 2 ); S 3 = S 1 ; (S 2 ; S 3 ) • The ``;'' operator is NOT commutative: • S 1 ; S 2 <> S 2 ; S 1

8. Communicating Hardware Processes • Parallel Operator • S 1 || S 2 means S 1 and S 2 are executed in • parallel. • The || operator is associative and commutative: • (S 1 || S 2 ) || S 3 = S 1 || (S 2 || S 3 ) • S 1 || S 2 = S 2 || S 1

9. Communicating Hardware Processes • Bullet Operator • S1.S2 means S1 and S2 complete simultaneously. • The . operator is associative and commutative: • (S 1 . S 2 ) . S 3 = S 1 . (S 2 . S 3 ) • S 1 . S 2 = S 2 . S 1

10. Communicating Hardware Processes • Other Properties • If S 1 and S 2 are non­interfering, • S 1 || S 2 is equivalent to the execution of either • S 1 ; S 2 or S 2 ; S 1 or S 1 . S 2 . • The operator precedence is: (1) . (2) ; (3) ||: • S 0 . S 1 ; S 2 || S 3 ===> ((S 0 . S 1 ); S 2 ) || S 3

11. Communicating Hardware Processes • Control Structures • Selection • Repetition • Deterministic and non­deterministic versions

12. Communicating Hardware Processes • Deterministic selection: • [G1 ==> S1 [] ... [] Gn ==> Sn ] • G1, ..., Gn are boolean expressions called guards. • S1 , ..., Sn are parts of a program, or commands. • Gi ==> Si :a guarded command • if Gi evaluates to true then Si is executed. • At any time, at most one guard is true. • If no guard is true, the execution is suspended. • Exact one guarded command will be executed

13. Communicating Hardware Processes • Non­deterministic selection: • [G1 ==> S1 | ... | Gn ==> Sn ] • Identical to deterministic selection except that • multiple guards can be true at the same time. • If multiple guards are true, one is selected • arbitrarily. • Exact one guarded command will be executed

14. Communicating Hardware Processes • Deterministic repetition: • *[G1 ==> S1 [] ... [] Gn ==> Sn ] • G1, ..., Gn are boolean expressions. • S1 , ..., Sn are parts of a program. • Gi ==> Si :a guarded command • if Gi evaluates to true then Si is executed. • After Si completes, control returns to the start. • At any time, at most one guard is true. • If no guard is true, the repetition terminates. • Zero, one or more guarded commands can be executed

15. Communicating Hardware Processes • Non­deterministic repetition: • *[G1 ==> S1 | ... | Gn ==> Sn ] • Identical to deterministic repetition except that • multiple guards can be true at the same time. • If multiple guards are true, one is selected • arbitrarily.

16. Communicating Hardware Processes • Wait command: • [G]= [G ==> skip] • Infinite repetition: • *[S] = *[true ==> S] • Reactive Process Structure • *[[G1 ==> S1 [] ... [] Gn ==> Sn ]] • Wait until some Gi holds; execute Si ; • repeat forever.

17. Communicating Hardware Processes • Replication Construct • Used to represent a list of syntactic objects. • <op i : n..m : S(i)> = • S(n), if n = m • S(n) op (<op i : n+1..m : S(i)>), if n < m • op is any constructor (;,.,||) or separator ([],|,``,'',`` ''), • i is an integer variable, called the running index, • the range, defined by n..m, where n and m are • integer constants, is not empty, i.e., n <= m, • S(i) is any program part in which i appears free.

18. Communicating Hardware Processes • Replication Construct • Example: • [<[] i : 0..3 : G(i) ==> S(i)>] = • [ G(0) ==> S(0) • [] G(1) ==> S(1) • [] G(2) ==> S(2) • [] G(3) ==> S(3) • ]

19. Communicating Hardware Processes • Procedures • Procedure parameters are either input or output. • Example: • procedure p(x : input; y : output); S • The procedure call p(a, b) is equivalent to: • x := a; S; b := y

20. Communicating Hardware Processes • Functions • Function parameters are always inputs. • Example: • function y(x); S • where S is the same program part as in • procedure p.

21. Communicating Hardware Processes • Concurrent Processes • Main building block of a computation is a process. • Body of a concurrent computation is of the form: • p1 || p2 || . . . || pn • where p1 through pn are processes. • Several instances of the same process type can • be called by assigning different names. • Unlike procedures, each instance of a process • can be called only once.

22. Communicating Hardware Processes • Communication Commands,Ports, & Channels • Processes communicate by using communication • commands on ports. • Ports are declared in the heading of a process: • p = process(R, L) • A port of a process is paired with a port of another • process to form a channel. • p1 =process(X) . . . end • p2 =process(Y) . . . end • p1 || p2 • chan(p1.X, p2.Y)

23. Communicating Hardware Processes • Example: • p1 =process(X) . . . end • p2 =process(Y) . . . end • p1 || p2 • chan(p1.X, p2.Y) • Equivalent to: • p1 =process(C) . . . end • p2 =process(C) . . . end • p1 || p2 • chan(C) X Y p1 p2 C p1 p2

24. Communicating Hardware Processes • Semantics of Synchronization • Number of completed receive actions cR cannot • exceed the number of completed send actions cS: • cR <= cS • Without buffering, if two processes p1 and p2 share • a channel with port X in p1 and port Y in p2 , then • cX = cY

25. Communicating Hardware Processes • Probe • If p1 reaches the n th X-action before p2 reaches • the n th Y-action, the completion of X is suspended • until p2 reaches Y. • The X-action is said to be pending. • The predicate ``X is pending'' is denoted qX. • The probe X in process p1 is the same value as qY.

26. Communicating Hardware Processes • Communication • Matching communication actions ``pass messages''. • X? is an input command on the input port X. • Y! is an output command on the output port Y. • X?u and Y!v implement the assignment v := u.

27. Communicating Hardware Processes Stream Merge: MERGE = process(X?int(8), Y?int(8), Z!int(8)) u : int(8) *[ [ X ==>X?u; Z!u | Y ==>Y?u; Z!u ] ]end Merge X Y Z

28. Communicating Hardware Processes One-place Buffer: BUF1=process(L?int(8), R!int(8)) x : int(8) *[L?x; R!x] end Buf L R

29. Communicating Hardware Processes N-place Buffer BUF(n) =process(L?int(8), R!int(8)) p(i : 0..n-1) : BUF1 <|| i : 0..n-1 : p(i)> chan<i : 0..n-2 : (p(i).R,p(i+1).L))> p(0).L = BUF(n).L p(n-1).R = BUF(n).R end Buf(n).L p(0).L P(0).R P(1).L P(n-1).R Buf(n).R P(1).R p(2).L P(0) P(1) P(n-1)

30. Communicating Hardware Processes Lazy Stack Stack element: Empty=[ in ==> in?x;Full [] out ==> get?x;out!x;Empty ] Full =[ out ==> out!x;Empty [] in ==> put!x;in?x;Full ] in out head put get out in Tail