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What kind of hypothesis might we think up Well, it could initially be as simple as the suspicion that a particular function or method is returning erroneous data when certain input data and options are used Then, if this hypothesis proves correct, we can re ne it to be more speci c for example, identifying a particular statement or suite in the function that we think is doing the wrong computation in certain cases To test our hypothesis we need to check the arguments that the function receives and the values of its local variables and the return value, immediately before it returns We can then run the program with data that we know produces errors and check the suspect function If the arguments coming into the function are not what we expect, then the problem is likely to be further up the call stack, so we would now begin the process again, this time suspecting the function that calls the one we have been looking at But if all the incoming arguments are always valid, then we must look at the local variables and the return value If these are always correct then we need to come up with a new hypothesis, since the suspect function is behaving correctly But if the return value is wrong, then we know that we must investigate the function further In practice, how do we conduct an experiment, that is, how do we test the hypothesis that a particular function is misbehaving One way to start is to execute the function mentally this is possible for many small functions and for larger ones with practice, and has the additional bene t that it familiarizes us with the function s behavior At best, this can lead to an improved or more speci c hypothesis for example, that a particular statement or suite is the site of the problem But to conduct an experiment properly we must instrument the program so that we can see what is going on when the suspect function is called There are two ways to instrument a program intrusively, by inserting print() statements; or (usually) non-intrusively, by using a debugger Both approaches are used to achieve the same end and both are valid, but some programmers have a strong preference for one or the other We ll brie y describe both approaches, starting with the use of print() statements When using print() statements, we can start by putting a print() statement right at the beginning of the function and have it print the function s arguments Then, just before the (or each) return statement (or at the end of the function if there is no return statement), add print(locals(), "\n") The builtin locals() function returns a dictionary whose keys are the names of the local variables and whose values are the variables values We can of course simply print the variables we are speci cally interested in instead Notice that we added an extra newline we should also do this in the rst print() statement so that a blank line appears between each set of variables to aid clarity (An alternative to inserting print() statements directly is to use some kind of logging decorator such as the one we created in 8; 358 ).

A parallel version of this program will be created by parallelizing the loop, using the Loop Parallelism pattern In this example, the shared data consists of the iparent and fitness arrays Within the body of the loop, calculations involving these arrays consist of swapping two elements of iparent and then swapping the corresponding elements of fitness Examination of these operations shows that two swap operations interfere when at least one of the locations being swapped is the same in both operations Thinking about the shared data as an ADT helps us to identify and analyze the actions taken on the shared data This does not mean, however, that the implementation itself always needs to reflect this structure In some cases, especially when the data structure is simple and the programming language does not support ADTs well, it can be more effective to forgo the encapsulation implied in an ADT and work with the data directly This example illustrates this As mentioned earlier, the chromosomes being swapped might interfere with each other; thus the loop over j cannot safely execute in parallel The most straightforward approach is to enforce a "one at a time" protocol using a critical section, as shown in Fig 535 It is also necessary to modify the random number generator so it produces a consistent set of pseudorandom numbers when called in parallel by many threads The algorithms to accomplish this are well understood [Mas97], but will not be discussed here

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