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Can the computational load be evenly balanced among the PEs This is easier if the tasks are independent, or if they are roughly the same size Is the overhead minimized Overhead can come from several sources, including creation and scheduling of the UEs, communication, and synchronization Creation and scheduling of UEs involves overhead, so each UE needs to have enough work to do to justify this overhead On the other hand, more UEs allow for better load balance Communication can also be a source of significant overhead, particularly on distributed memory platforms that depend on message passing As we discussed in Section 26, the time to transfer a message has two components: latency cost arising from operating system overhead and message start up costs on the network, and a cost that scales with the length of the message To minimize the latency costs, the number of messages to be sent should be kept to a minimum In other words, a small number of large messages is better than a large number of small ones The second term is related to the bandwidth of the network These costs can sometimes be hidden by overlapping communication with computation On shared memory machines, synchronization is a major source of overhead When data is shared between UEs, dependencies arise requiring one task to wait for another to avoid race conditions The synchronization mechanisms used to control this waiting are expensive compared to many operations carried out by a UE Furthermore, some synchronization constructs generate significant memory traffic as they flush caches, buffers, and other system resources to make sure UEs see a consistent view of memory This extra memory traffic can interfere with the explicit data movement within a computation Synchronization overhead can be reduced by keeping data well localized to a task, thereby minimizing the frequency of synchronization operations.

format()

Now that you have documented the process as a use case, you have the building blocks necessary to create a use case diagram A use case diagram is a visual representation of how a system functions Each process, or use

If a conversion fails, we output the line number (starting from line 1 as is traditional for text les), the text we attempted to convert, and the ValueError exception s error text Rather than using positional arguments (eg, format(filename, lino, etc, or explicitly named arguments, format(filename=filename, lino=lino, etc), we have retrieved the names and values of the local variables by calling locals() and used mapping unpacking to pass these as key value named arguments to the strformat() method

def calculate_statistics(numbers, frequencies): mean = sum(numbers) / len(numbers) mode = calculate_mode(frequencies, 3) median = calculate_median(numbers) std_dev = calculate_std_dev(numbers, mean) return Statistics(mean, mode, median, std_dev)

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Simplicity To paraphrase Einstein: Make it as simple as possible, but not simpler Keep in mind that practically all programs will eventually need to be debugged, maintained, and often enhanced and ported A design even a generally superior design is not valuable if it is too hard to debug, maintain, and verify the correctness of the final program The medical imaging example initially described in Sec 313 and then discussed further in the Task Decomposition and Data Decomposition patterns is an excellent case in point in support of the value

This function is used to gather all the statistics together Because the mean ( average ) is so easy to calculate, we do so directly here For the other statistics we call dedicated functions, and at the end we return a Statistics named tuple object that contains the four statistics we have calculated

def calculate_mode(frequencies, maximum_modes): highest_frequency = max(frequenciesvalues()) mode = [number for number, frequency in frequenciesitems() if frequency == highest_frequency] if not (1 <= len(mode) <= maximum_modes): mode = None else: modesort() return mode

5

of simplicity In this problem, a large database could be decomposed, but this decomposition would force the parallel algorithm to include complex operations for passing trajectories between UEs and to distribute chunks of the database This complexity makes the resulting program much more difficult to understand and greatly complicates debugging The other approach, replicating the database, leads to a vastly simpler parallel program in which completely independent tasks can be passed out to multiple workers as they are read All complex communication thus goes away, and the parallel part of the program is trivial to debug and reason about

There may be more than one most-frequently-occurring number, so in addition to the dictionary of frequencies, this function also requires the caller to specify the maximum number of modes that are acceptable (The calculate_statistics() function is the caller, and it speci ed a maximum of three modes) The max() function is used to nd the highest value in the frequencies dictionary Then, we use a list comprehension to create a list of those modes whose frequency equals the highest value We can compare using operator == since all the frequencies are integers

If the number of modes is 0 or greater than the maximum modes that are acceptable, a mode of None is returned; otherwise, a sorted list of the modes is returned

def calculate_median(numbers): numbers = sorted(numbers) middle = len(numbers) // 2 median = numbers[middle] if len(numbers) % 2 == 0: median = (median + numbers[middle - 1]) / 2 return median

The problem decomposition carried out with the Finding Concurrency patterns defines the key components that will guide the design in the Algorithm Structure design space:

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