Other Built-in Numeric Tools

In addition to its core object types, Python also provides both built-in functions and standard library modules for numeric processing. The pow and abs built-in functions, for instance, compute powers and absolute values, respectively. Here are some examples of the built-in math module (which contains most of the tools in the C language’s math library) and a few built-in functions at work:

>>> import math
>>> math.pi, math.e                               # Common constants
(3.1415926535897931, 2.7182818284590451)

>>> math.sin(2 * math.pi / 180)                   # Sine, tangent, cosine
0.034899496702500969

>>> math.sqrt(144), math.sqrt(2)                  # Square root
(12.0, 1.4142135623730951)

>>> pow(2, 4), 2 ** 4                             # Exponentiation (power)
(16, 16)

>>> abs(-42.0), sum((1, 2, 3, 4))                 # Absolute value, summation
(42.0, 10)

>>> min(3, 1, 2, 4), max(3, 1, 2, 4)              # Minimum, maximum
(1, 4)

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The sum function shown here works on a sequence of numbers, and min and max accept either a sequence or individual arguments. There are a variety of ways to drop the decimal digits of floating-point numbers. We met truncation and floor earlier; we can also round, both numerically and for display purposes:

>>> math.floor(2.567), math.floor(-2.567)         # Floor (next-lower integer)
(2, −3)

>>> math.trunc(2.567), math.trunc(−2.567)         # Truncate (drop decimal digits)
(2, −2)

>>> int(2.567), int(−2.567)                       # Truncate (integer conversion)
(2, −2)

>>> round(2.567), round(2.467), round(2.567, 2)   # Round (Python 3.0 version)
(3, 2, 2.5699999999999998)

>>> '%.1f' % 2.567, '{0:.2f}'.format(2.567)       # Round for display (Chapter 7)
('2.6', '2.57')

As we saw earlier, the last of these produces strings that we would usually print and supports a variety of formatting options. As also described earlier, the second to last test here will output (3, 2, 2.57) if we wrap it in a print call to request a more user-friendly display. The last two lines still differ, though—round rounds a floating-point number but still yields a floating-point number in memory, whereas string formatting produces a string and doesn’t yield a modified number:

>>> (1 / 3), round(1 / 3, 2), ('%.2f' % (1 / 3))
(0.33333333333333331, 0.33000000000000002, '0.33')

Interestingly, there are three ways to compute square roots in Python: using a module function, an expression, or a built-in function (if you’re interested in performance, we will revisit these in an exercise and its solution at the end of Part IV, to see which runs quicker):

>>> import math
>>> math.sqrt(144)              # Module
12.0
>>> 144 ** .5                   # Expression
12.0
>>> pow(144, .5)                # Built-in
12.0

>>> math.sqrt(1234567890)       # Larger numbers
35136.418286444619
>>> 1234567890 ** .5
35136.418286444619
>>> pow(1234567890, .5)
35136.418286444619

Notice that standard library modules such as math must be imported, but built-in functions such as abs and round are always available without imports. In other words, modules are external components, but built-in functions live in an implied namespace that Python automatically searches to find names used in your program. This namespace corresponds to the module called builtins in Python 3.0 (__builtin__ in 2.6). There is much more about name resolution in the function and module parts of this book; for now, when you hear “module,” think “import.”

The standard library random module must be imported as well. This module provides tools for picking a random floating-point number between 0 and 1, selecting a random integer between two numbers, choosing an item at random from a sequence, and more:

>>> import random
>>> random.random()
0.44694718823781876
>>> random.random()
0.28970426439292829

>>> random.randint(1, 10)
5
>>> random.randint(1, 10)
4

>>> random.choice(['Life of Brian', 'Holy Grail', 'Meaning of Life'])
'Life of Brian'
>>> random.choice(['Life of Brian', 'Holy Grail', 'Meaning of Life'])
'Holy Grail'

The random module can be useful for shuffling cards in games, picking images at random in a slideshow GUI, performing statistical simulations, and much more. For more details, see Python’s library manual.

 

[15] If you’re working along, you don’t need to type any of the comment text from the # through to the end of the line; comments are simply ignored by Python and not required parts of the statements we’re running.