Decimal Type

Python 2.4 introduced a new core numeric type: the decimal object, formally known as Decimal. Syntactically, decimals are created by calling a function within an imported module, rather than running a literal expression. Functionally, decimals are like floating-point numbers, but they have a fixed number of decimal points. Hence, decimals are fixed-precision floating-point values.

For example, with decimals, we can have a floating-point value that always retains just two decimal digits. Furthermore, we can specify how to round or truncate the extra decimal digits beyond the object’s cutoff. Although it generally incurs a small performance penalty compared to the normal floating-point type, the decimal type is well suited to representing fixed-precision quantities like sums of money and can help you achieve better numeric accuracy.

广告：个人专属 VPN，独立 IP，无限流量，多机房切换，还可以屏蔽广告和恶意软件，每月最低仅 5 美元

The basics

The last point merits elaboration. As you may or may not already know, floating-point math is less than exact, because of the limited space used to store values. For example, the following should yield zero, but it does not. The result is close to zero, but there are not enough bits to be precise here:

>>> 0.1 + 0.1 + 0.1 - 0.3
5.5511151231257827e-17

Printing the result to produce the user-friendly display format doesn’t completely help either, because the hardware related to floating-point math is inherently limited in terms of accuracy:

>>> print(0.1 + 0.1 + 0.1 - 0.3)
5.55111512313e-17

However, with decimals, the result can be dead-on:

>>> from decimal import Decimal
>>> Decimal('0.1') + Decimal('0.1') + Decimal('0.1') - Decimal('0.3')
Decimal('0.0')

As shown here, we can make decimal objects by calling the Decimal constructor function in the decimal module and passing in strings that have the desired number of decimal digits for the resulting object (we can use the str function to convert floating-point values to strings if needed). When decimals of different precision are mixed in expressions, Python converts up to the largest number of decimal digits automatically:

>>> Decimal('0.1') + Decimal('0.10') + Decimal('0.10') - Decimal('0.30')
Decimal('0.00')

Note

In Python 3.1 (to be released after this book’s publication), it’s also possible to create a decimal object from a floating-point object, with a call of the form decimal.Decimal.from_float(1.25). The conversion is exact but can sometimes yield a large number of digits.

Setting precision globally

Other tools in the decimal module can be used to set the precision of all decimal numbers, set up error handling, and more. For instance, a context object in this module allows for specifying precision (number of decimal digits) and rounding modes (down, ceiling, etc.). The precision is applied globally for all decimals created in the calling thread:

>>> import decimal
>>> decimal.Decimal(1) / decimal.Decimal(7)
Decimal('0.1428571428571428571428571429')

>>> decimal.getcontext().prec = 4
>>> decimal.Decimal(1) / decimal.Decimal(7)
Decimal('0.1429')

This is especially useful for monetary applications, where cents are represented as two decimal digits. Decimals are essentially an alternative to manual rounding and string formatting in this context:

>>> 1999 + 1.33
2000.3299999999999
>>>
>>> decimal.getcontext().prec = 2
>>> pay = decimal.Decimal(str(1999 + 1.33))
>>> pay
Decimal('2000.33')

Decimal context manager

In Python 2.6 and 3.0 (and later), it’s also possible to reset precision temporarily by using the with context manager statement. The precision is reset to its original value on statement exit:

C:\misc> C:\Python30\python
>>> import decimal
>>> decimal.Decimal('1.00') / decimal.Decimal('3.00')
Decimal('0.3333333333333333333333333333')
>>>
>>> with decimal.localcontext() as ctx:
...     ctx.prec = 2
...     decimal.Decimal('1.00') / decimal.Decimal('3.00')
...
Decimal('0.33')
>>>
>>> decimal.Decimal('1.00') / decimal.Decimal('3.00')
Decimal('0.3333333333333333333333333333')

Though useful, this statement requires much more background knowledge than you’ve obtained at this point; watch for coverage of the with statement in Chapter 33.

Because use of the decimal type is still relatively rare in practice, I’ll defer to Python’s standard library manuals and interactive help for more details. And because decimals address some of the same floating-point accuracy issues as the fraction type, let’s move on to the next section to see how the two compare.