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In computer science, a for-loop or for loop is a control flow statement for specifying iteration. Specifically, a for-loop functions by running a section of code repeatedly until a certain condition has been satisfied.
In mathematics, iteration may refer to the process of iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences.
The iteration form of the Eiffel loop can also be used as a boolean expression when the keyword loop is replaced by either all (effecting universal quantification) or some (effecting existential quantification). This iteration is a boolean expression which is true if all items in my_list have counts greater than three:
In this example, there is a true dependence between the j iteration of statement S1 and the j+1th statement of S1. This can be represented as S1[i,j] →T S1[i,j+1] The iteration space traversal graph and the loop carried dependence graph is: Iteration Space Traversal Graph: Loop Carried Dependence Graph:
Because the notation f n may refer to both iteration (composition) of the function f or exponentiation of the function f (the latter is commonly used in trigonometry), some mathematicians [citation needed] choose to use ∘ to denote the compositional meaning, writing f ∘n (x) for the n-th iterate of the function f(x), as in, for example, f ...
For example, the iterator method is supposed to return an Iterator object, and the pull-one method is supposed to produce and return the next value if possible, or return the sentinel value IterationEnd if no more values could be produced. The following example shows an equivalent iteration over a collection using explicit iterators:
In loop-carried dependence, statements in an iteration of a loop depend on statements in another iteration of the loop. Loop-Carried Dependence uses a modified version of the dependence notation seen earlier. Example of loop-carried dependence where S1[i] ->T S1[i + 1], where i indicates the current iteration, and i + 1 indicates the next ...
Loop interchange on this example can improve the cache performance of accessing b(j,i), but it will ruin the reuse of a(i) and c(i) in the inner loop, as it introduces two extra loads (for a(i) and for c(i)) and one extra store (for a(i)) during each iteration. As a result, the overall performance may be degraded after loop interchange.