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Decimal numbers are created using the decimalDecimal() function This function can take an integer or a string argument but not a float, since floats are held inexactly whereas decimals are represented exactly If a string is used it can use simple decimal notation or exponential notation In addition to providing accuracy, the exact representation of decimalDecimals means that they can be reliably compared for equality From Python 31 it is possible to convert floats to decimals using the decimalDecimalfrom_float() function This function takes a float as argument and returns the decimalDecimal that is closest to the number the float approximates All the numeric operators and functions listed in Table 22 (55 ), including the augmented assignment versions, can be used with decimalDecimals, but with a couple of caveats If the ** operator has a decimalDecimal left-hand operand, its right-hand operand must be an integer Similarly, if the pow() function s rst argument is a decimalDecimal, then its second and optional third arguments must be integers The math and cmath modules are not suitable for use with decimalDecimals, but some of the functions provided by the math module are provided as decimalDecimal methods For example, to calculate ex where x is a float, we write mathexp(x), but where x is a decimalDecimal, we write xexp() From the discussion in Piece #3 (20 ), we can see that xexp() is, in effect, syntactic sugar for decimalDecimalexp(x) The decimalDecimal data type also provides ln() which calculates the natural (base e) logarithm (just like mathlog() with one argument), log10(), and sqrt(), along with many other methods speci c to the decimalDecimal data type Numbers of type decimalDecimal work within the scope of a context; the context is a collection of settings that affect how decimalDecimals behave The context speci es the precision that should be used (the default is 28 decimal places), the rounding technique, and some other details In some situations the difference in accuracy between floats and decimal.

Decimals becomes obvious: >>> 23 / 105 21904761904761905 >>> print(23 / 105) 219047619048 >>> print(decimalDecimal(23) / decimalDecimal("105")) 2190476190476190476190476190

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Flexibility The design needs to be flexible in the number of tasks generated Usually this is done by parameterizing the number and size of tasks on some appropriate dimension This will let the design be adapted to a wide range of parallel computers with different numbers of processors Efficiency There are two major efficiency issues to consider in the task decomposition First, each task must include enough work to compensate for the overhead incurred by creating the tasks and managing their dependencies Second, the number of tasks should be large enough so that all the units of execution are busy with useful work throughout the computation Simplicity Tasks should be defined in a way that makes debugging and maintenance simple When possible, tasks should be defined so they reuse code from existing sequential programs that solve related problems

>>> decimalDecimal(23) / decimalDecimal("105") Decimal('2190476190476190476190476190')

As with primary keys, foreign keys in SQL Server work in the same way as they do in logical design A foreign key is the column or columns that correspond to a primary key and establish a relationship Exactly the same columns with the same data as the primary key exist in the foreign key It

Although the division using decimalDecimals is more accurate than the one involving floats, in this case (on a 32-bit machine) the difference only shows up in the fteenth decimal place In many situations this is insigni cant for example, in this book, all the examples that need oating-point numbers use floats One other point to note is that the last two of the preceding examples reveal for the rst time that printing an object involves some behind-the-scenes formatting When we call print() on the result of decimalDecimal(23) / decimalDecimal("105") the bare number is printed this output is in string form If we simply enter the expression we get a decimalDecimal output this output is in representational form All Python objects have two output forms String form is designed to be human-readable Representational form is designed to produce output that if fed to a Python interpreter would (when possible) reproduce the represented object We will return to this topic in the next section where we discuss strings, and again in 6 when we discuss providing string and representational forms for our own custom data types The Library Reference s decimal module documentation provides all the details that are too obscure or beyond our scope to cover; it also provides more examples, and a FAQ list

Strings are represented by the immutable str data type which holds a sequence of Unicode characters The str data type can be called as a function to create string objects with no arguments it returns an empty string, with a nonstring argument it returns the string form of the argument, and with a string argument it returns a copy of the string The str() function can also be used as a conversion function, in which case the rst argument should be a string or something convertable to a string, with up to two optional string arguments being passed, one specifying the encoding to use and the other specifying how to handle encoding errors Earlier we mentioned that string literals are created using quotes, and that we are free to use single or double quotes providing we use the same at both ends In addition, we can use a triple quoted string this is Python-speak for a string that begins and ends with three quote characters (either three single quotes or three double quotes) For example:

After the tasks have been identified, the next step is to look at the data decomposition implied by the tasks The Data Decomposition pattern may help with this analysis Examples

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