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One problem that the decorator faces is that class object from which every other class is ultimately derived de nes all six comparison operators, all of which raise a TypeError exception if used So we need to know whether < and == have been reimplemented (and are therefore usable) This can easily be done by comparing the relevant special methods in the class being decorated with those in object If the decorated class does not have a custom < the assertion fails because that is the decorator s minimum requirement And if there is a custom == we use it; otherwise, we create one Then all the other methods are created and the decorated class, now with all six comparison methods, is returned Using class decorators is probably the simplest and most direct way of changing classes Another approach is to use metaclasses, a topic we will cover later in this chapter

This is an extreme example, but you can see how SQL Server would have no idea you have a table named INSERT with columns named where, and, name, and date You would receive a syntax error when compiling this code, and you would need to surround all the keywords with square brackets, as follows This fixes the syntax problems but doesn t make it any easier for a person to read

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An abstract base class (ABC) is a class that cannot be used to create objects Instead, the purpose of such classes is to de ne interfaces, that is, to in effect list the methods and properties that classes that inherit the abstract base class must provide This is useful because we can use an abstract base class as a kind of promise a promise that any derived class will provide the methods and properties that the abstract base class speci es

some degree of nonuniformity in memory access times across the system In many cases, these effects are of secondary concern, and we can ignore how a program's memory access patterns match up with the target system's memory hierarchy In other cases, particularly on larger shared memory machines, programs must be explicitly organized according to the needs of the memory hierarchy The most common trick is to make sure the data access patterns during initialization of key data structures match those during later computation using these data structures This is discussed in more detail in [Mat03, NA01] and later in this pattern as part of the mesh computation example Another performance problem is false sharing This occurs when variables are not shared between UEs, but happen to reside on the same cache line Hence, even though the program semantics implies independence, each access by each UE requires movement of a cache line between UEs This can create huge overheads as cache lines are repeatedly invalidated and moved between UEs as these supposedly independent variables are updated An example of a program fragment that would incur high levels of false sharing is shown in Fig 523 In this code, we have a pair of nested loops The outermost loop has a small iteration count that will map onto the number of UEs (which we assume is four in this case) The innermost loop runs over a large number of time consuming iterations Assuming the iterations of the innermost loop are roughly equal, this loop should parallelize effectively But the updates to the elements of the A array inside the innermost loop mean each update requires the UE in question to own the indicated cache line Although the elements of A are truly independent between UEs, they likely sit in the same cache line Hence, every iteration in the innermost loop incurs an expensive cache line invalidate and movement operation It is not uncommon for this to not only destroy all parallel speedup, but to even cause the parallel program to become slower as more PEs are added The solution is to create a temporary variable on each thread to accumulate values in the innermost loop False sharing is still a factor, but only for the much smaller outermost loop where the performance impact is negligible.

Python s abstract base classes are described in PEP 3119 (wwwpythonorg/dev/peps/pep-3119), which also includes a very useful rationale and is well worth reading

complex, decimalDecimal, float, fractionsFraction, int ==, !=, +, -, *, /, abs(), bool(), complex, complex(), conjugate(); also real decimalDecimal, and imag properties float, fractionsFraction, int <, <=, ==, !=, >=, >, +, -, *, /, decimalDecimal, //, %, abs(), bool(), complex(), float, conjugate(), divmod(), float(), fractionsFraction, mathceil(), mathfloor(), round(), int trunc(); also real and imag

SELECT [where], [and], name, date FROM [INSERT] WHERE [and] = 1 AND [where] = 'Omaha'

Figure 523 Program fragment showing an example of false sharing The small array A is held in one or two cache lines As the UEs access A inside the innermost loop, they will need to take ownership of the cache line back from the other UEs This back-andforth movement of the cache lines destroys performance The solution is to use a temporary variable inside the innermost loop

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