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A number of so-called single-assignment languages have been developed over the years, many designed for parallel scientiﬁc computing. Single-assignment conditions are also used in program optimization and in hardware description languages. Single-assignment conditions arise in hardware as only one assignment to each variable may occur per clock cycle.
One example of a single-assignment language is SISAL, which stands for streams and iteration in a single-assignment language. Another is SAC, or single- assignment C. Programs in single-assignment languages must satisfy the following condition:
During any run of the program, each variable may be assigned a value only once, within the scope of the variable.
The following program fragment satisﬁes this condition,
if (y>3) then x = 42+29/3 else x = 13.39;
because only one branch of the if-then-else will be executed on any run of the program. The program x=2; loop forever; x=3 also satisﬁes the condition because no execution will complete both assignments.
Single-assignment languages often have specialized loop constructs, as other- wise it would be impossible to execute an assignment inside a loop body that gets executed more than once. Here is one form, from SISAL:
for (range) (body)
returns (returns clause) end for
An example illustrating this form is the following loop, which computes the dot (or inner) product of two vectors
for i in 1, size
elt prod := x[i]∗y[i] returns value of sum elt prod end for
This loop is parallelizable because different products x[i]∗y[i] can be computed in parallel. A typical SISAL program has a sequential outer loop containing a set of parallel loops.
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Suppose you have the job of building a parallelizing compiler for a single- assignment language. Assume that the programs you compile satisfy the single- assignment condition and do not contain any explicit process fork or other parallelizing instructions. Your implementation must ﬁnd parts of programs that can be safely executed in parallel, producing the same output values as if the program were executed sequentially on a single processor.
Assume for simplicity that every variable is assigned a value before the value of the variable is used an in expression. Also assume that there is no potential source of side effects in the language other than assignment.
(a) Explain how you might execute parts of the sample program
y = f(g(x),h(x));
if y==5 then z=g(x) else z=h(x);
in parallel. More speciﬁcally, assume that your implementation will schedule the following processes in some way:
process 1 – set x to 5 process 2 – call g(x) process 3 – call h(x)
process 4 – call f(g(x),h(x)) and set y to this value process 5 – test y==5
process 6 – call g(x) and then set z=g(x) process 7 – call h(x) and then set z=h(x)
For each process, list the processes that this process must wait for and list the processes that can be executed in parallel with it. For simplicity, assume that a call cannot be executed until the parameters have been evaluated and assume that processes 6 and 7 are not divided into smaller processes that execute the calls but do not assign to z. Assume that parameter passing in the example code is by value.
(b) If you further divide process 6 into two processes, one that calls g(x) and one that assigns to z, and similarly divide process 7 into two processes, can you execute the calls g(x) and h(x) in parallel? Could your compiler correctly eliminate these calls from processes 6 and 7? Explain brieﬂy.
(c) Would the parallel execution of processes you describe in parts (a) and (b), if any, be correct if the program does not satisfy the single-assignment condition? Explain brieﬂy.
(d) Is the single-assignment condition decidable? Speciﬁcally, given an program written in asubset of C, for concreteness, is it possible for acompiler to decide whether this program satisﬁes the single-assignment condition? Explain why or why not. If not, can you think of a decidable condition that implies the single- assignment condition and allows many useful single-assignment programs to be recognized?
(e) Suppose a single-assignment language has no side-effect operations other than assignment. Does this language pass the declarative language test? Explain why or why not.
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