Dependence Analysis Important and difficult Parallelize Optimize memory hierarchy Loop --- and non-loops ? Application to program transformation Should yield “better” code Should NOT alter code semantics atof( ) - converts the "character string" pointed to by nptr to a double and returns its value atol( ) - converts the "character string" pointed to by str to a long and returns its value atoi( ) - converts the "character string" pointed to by str to an int

Which Loop(s) Parallelizable ? 1) Do I = 1, n A[I] = 5 * B[I] + A[I] Enddo 2) Do I = 1, n A[I-1] = 5 * B[I] + A[I] Enddo 3) Do I = 1, n temp = 5 * B[I] A[I] = temp Enddo 4) Do I = 1, n A[I+1] = 5 * B[I] + A[I] Enddo

Data Dependence Statement S2 is dependent on S1 iff Dependence “types” S2 follows S1 in execution S2, S1 access same memory location, M One of S2 or S1 write to M Dependence “types” True (or flow) -- S2 reads M set by S1 Anti- -- S2 writes M read by S1 Output -- S1 and S2 write M Dependence Graph

Example S1: a = 3.14 S2: b = 5.0 S3: c = a * b * b S1 S2 S3

Example S1: a = 3.14 S1 S2 S2: b = 5.0 S3: c = a * b * b S4: b = a * c

Program Order, Dependence Sequential order of imperative programs is too restrictive Partial order of dependences needed to ensure “correctness” Reordering transformations should not violate dependence Can we always determine dependence?

Dependence in Loops Parameterize stmts by loop iterations Loop nesting level: number of surrounding loops + 1 Iteration number: value of iteration (index) variable Iteration vector, I, of loop is the value of all index variables for outer loop(s) for a particular iteration of innermost loop Iteration space is set of all possible iteration vectors for a statement