By Samuel P. Midkiff

Compiling for parallelism is a longstanding subject of compiler study. This ebook describes the elemental ideas of compiling "regular" numerical courses for parallelism. we start with a proof of analyses that let a compiler to appreciate the interplay of knowledge reads and writes in numerous statements and loop iterations in the course of application execution. those analyses comprise dependence research, use-def research and pointer research. subsequent, we describe how the result of those analyses are used to allow changes that make loops extra amenable to parallelization, and speak about differences that disclose parallelism to focus on shared reminiscence multicore and vector processors. We then talk about a few difficulties that come up whilst parallelizing courses for execution on disbursed reminiscence machines. eventually, we finish with an outline of fixing Diophantine equations and proposals for extra readings within the themes of this booklet to let the reader to delve deeper into the sector.

desk of Contents: advent and evaluate / Dependence research, dependence graphs and alias research / application parallelization / changes to change and do away with dependences / Transformation of iterative and recursive constructs / Compiling for disbursed reminiscence machines / fixing Diophantine equations / A consultant to extra interpreting

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B) The CFG for the program of (a) initialized to begin the constant propagation dataflow analysis. (d) The CFG after the second pass—the dataflow information has converged. 2: An example of a flow sensitive constant propagation analysis. 21 22 2. DEPENDENCE ANALYSIS, DEPENDENCE GRAPHS AND ALIAS ANALYSIS Constant propagation is a forward data flow analysis, that is, facts that are true at some point are propagated forward through the program. The program state, before a statement is executed, is in the IN set, and the program state after the statement is executed is in the OUT set.

Banerjee’s inequalities were the earliest such heuristic. They attempt to find an upper and lower bound on the right-hand side of the equation. Consider a term a ∗ i − b ∗ i in the right-hand side. If the direction vector is 1, then i < i , and thus the lower bound of the term (assuming a, b positive) is a ∗ lbi − b ∗ ubi . 3. DATA DEPENDENCE ANALYSIS 37 of a > 0, b < 0; a < 0, b > 0, and a < 0, b < 0. From these the minimum (L) and maximum (U) values of the dependence equation can be found, and by the mean value theorem, if L ≤ b0 − a0 ≤ U , the equation is assumed to have a solution in the iteration space, and a dependence is assumed to exist.

DATA DEPENDENCE ANALYSIS 37 of a > 0, b < 0; a < 0, b > 0, and a < 0, b < 0. From these the minimum (L) and maximum (U) values of the dependence equation can be found, and by the mean value theorem, if L ≤ b0 − a0 ≤ U , the equation is assumed to have a solution in the iteration space, and a dependence is assumed to exist. If it is not the case that if L ≤ b0 − a0 ≤ U then dependence has been disproved. , nests in which the upper and lower bounds of all loops are constants within the iteration space) with known loop bounds, this test is precise [22].