Description
Loop dependence analysis occur on a normalized loop of the form:
for i1 until U1 do for i2 until U2 do ... for in until Un do body done done
done
where body may contain:
S1 a := ... ...
S2 ... := a
Where a is an m-dimensional array and fn, hn, etc. are functions mapping from all iteration indexes (in) to a memory access in a particular dimension of the array.
For example, in C:
for (i = 0; i < U1; i++) for (j = 0; j < U2; j++) a = b + i*j;f1 would be i+4-j, controlling the write on the first dimension of a and h2 would be 2*i-j, controlling the read on the first dimension of b.
The scope of the problem is to find all possible dependencies between S1 and S2. To be conservative, any dependence which cannot be proven false must be assumed to be true.
Independence is shown by demonstrating that no two instances of S1 and S2 access or modify the same spot in array a. When a possible dependence is found, loop dependence analysis usually makes every attempt to characterize the relationship between dependent instances, as some optimizations may still be possible. It may also be possible to transform the loop to remove or modify the dependence.
In the course of (dis)proving such dependencies, a statement S may be decomposed according to which iteration it comes from. For instance, S refers to the iteration where i1 = 1, i2 = 3 and i3 = 5. Of course, references to abstract iterations, such as S, are both permitted and common.
Read more about this topic: Loop Dependence Analysis
Famous quotes containing the word description:
“Why does philosophy use concepts and why does faith use symbols if both try to express the same ultimate? The answer, of course, is that the relation to the ultimate is not the same in each case. The philosophical relation is in principle a detached description of the basic structure in which the ultimate manifests itself. The relation of faith is in principle an involved expression of concern about the meaning of the ultimate for the faithful.”
—Paul Tillich (1886–1965)
“The type of fig leaf which each culture employs to cover its social taboos offers a twofold description of its morality. It reveals that certain unacknowledged behavior exists and it suggests the form that such behavior takes.”
—Freda Adler (b. 1934)
“God damnit, why must all those journalists be such sticklers for detail? Why, they’d hold you to an accurate description of the first time you ever made love, expecting you to remember the color of the room and the shape of the windows.”
—Lyndon Baines Johnson (1908–1973)