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# Native Datatypes

> ❝ Wonder is the foundation of all philosophy, inquiry its progress, ignorance its end. ❞
> — Michel de Montaigne

## Diving In

Cast aside your first Python program for just a minute, and let’s talk about datatypes. In Python, every variable has a datatype, but you don’t need to declare it explicitly. Based on each variable’s original assignment, Python figures out what type it is and keeps tracks of that internally.

Python has many native datatypes. Here are the important ones:

1. Booleans are either `True` or `False`.
2. Numbers can be integers (`1` and `2`), floats (`1.1` and `1.2`), fractions (`1/2` and `2/3`), or even complex numbers (`i`, the square root of `-1`).
3. Strings are sequences of Unicode characters, e.g. an HTML document.
4. Bytes and byte arrays, e.g. a JPEG image file.
5. Lists are ordered sequences of values.
6. Sets are unordered bags of values.
7. Dictionaries are unordered bags of key-value pairs.

Of course, there are a lot more types than these seven. Everything is an object in Python, so there are types like module, function, class, method, file, and even compiled code. You’ve already seen some of these: modules have names, functions have `docstrings`, &c. You’ll learn about classes in [FIXME xref] and files in [FIXME xref].

Strings and bytes are important enough — and complicated enough — that they get their own chapter. Let’s look at the others first.

## Booleans

You can use virtually any expression in a boolean context.

Booleans are either true or false. Python has two constants, `True` and `False`, which can be used to assign boolean values directly. Expressions can also evaluate to a boolean value. In certain places (like `if` statements), Python expects an expression to evaluate to a boolean value. These places are called boolean contexts. You can use virtually any expression in a boolean context, and Python will try to determine its truth value. Different datatypes have different rules about which values are true or false in a boolean context. (This will make more sense once you see some concrete examples later in this chapter.)

For example, take this snippet from `humansize.py`:

    if size < 0:
        raise ValueError('number must be non-negative')

size is an integer, `0` is an integer, and `<` is a numerical operator. The result of the expression `size < 0` is always a boolean. You can test this yourself in the Python interactive shell:

    >>> size = 1
    >>> size < 0
    False
    >>> size = 0
    >>> size < 0
    False
    >>> size = -1
    >>> size < 0
    True

## Numbers

Numbers are awesome. There are so many to choose from. Python supports both integers and floating point numbers. There’s no type declaration to distinguish them; Python tells them apart by the presence or absence of a decimal point.

    >>> type(1)                 ①
    <class 'int'>
    >>> 1 + 1                   ②
    2
    >>> 1 + 1.0                 ③
    2.0
    >>> type(2.0)
    <class 'float'>

1. You can use the `type()` function to check the type of any value or variable. As you might expect, `1` is an `int`.
2. Adding an `int` to an `int` yields an `int`.
3. Adding an `int` to a `float` yields a `float`. Python coerces the `int` into a `float` to perform the addition, then returns a `float` as the result.

### Coercing Integers To Floats And Vice-Versa

As you just saw, some operators (like addition) will coerce integers to floating point numbers as needed. You can also coerce them by yourself.

    >>> float(2)                ①
    2.0
    >>> int(2.0)                ②
    2
    >>> int(2.5)                ③
    2
    >>> int(-2.5)               ④
    -2
    >>> 1.12345678901234567890  ⑤
    1.1234567890123457
    >>> type(1000000000000000)  ⑥
    <class 'int'>

1. You can explicitly coerce an `int` to a `float` by calling the `float()` function.
2. Unsurprisingly, you can also coerce a `float` to an `int` by calling `int()`.
3. The `int()` function will truncate, not round.
4. The `int()` function truncates negative numbers towards `0`. It’s a true truncate function, not a a floor function.
5. Floating point numbers are accurate to 15 decimal places.
6. Integers can be arbitrarily large.

> ☞Python 2 had separate types for `int` and `long`. The `int` datatype was limited by `sys.maxint`, which varied by platform but was usually `232-1`. Python 3 has just one integer type, which behaves mostly like the old `long` type from Python 2. See PEP 237 for details.

### Common Numerical Operations

You can do all kinds of things with numbers.

    >>> 11 / 2      ①
    5.5
    >>> 11 // 2     ②
    5
    >>> −11 // 2    ③
    −6
    >>> 11.0 // 2   ④
    5.0
    >>> 11 ** 2     ⑤
    121
    >>> 11 % 2      ⑥
    1

1. The `/` operator performs floating point division. It returns a `float` even if both the numerator and denominator are `int`s.
2. The `//` operator performs a quirky kind of integer division. When the result is positive, you can think of it as truncating (not rounding) to `0` decimal places, but be careful with that.
3. When integer-dividing negative numbers, the `//` operator rounds “up” to the nearest integer. Mathematically speaking, it’s rounding “down” since `−6` is less than `−5`, but it could trip you up if you expecting it to truncate to `−5`.
4. The `//` operator doesn’t always return an integer. If either the numerator or denominator is a `float`, it will still round to the nearest integer, but the actual return value will be a `float`.
5. The `**` operator means “raised to the power of.” `112` is `121`.
6. The `%` operator gives the remainder after performing integer division. `11` divided by `2` is `5` with a remainder of `1`, so the result here is `1`.

> ☞In Python 2, the `/` operator usually meant integer division, but you could make it behave like floating point division by including a special directive in your code. In Python 3, the `/` operator always means floating point division. See PEP 238 for details.

### Fractions

Python isn’t limited to integers and floating point numbers. It can also do all the fancy math you learned in high school and promptly forgot about.

    >>> import fractions              ①
    >>> x = fractions.Fraction(1, 3)  ②
    >>> x
    Fraction(1, 3)
    >>> x * 2                         ③
    Fraction(2, 3)
    >>> fractions.Fraction(6, 4)      ④
    Fraction(3, 2)

1. To start using fractions, import the `fractions` module.
2. To define a fraction, create a `Fraction` object and pass in the numerator and denominator.
3. You can perform all the usual mathematical operations with fractions. Operations return a new `Fraction` object. `2 * (1/3) = (2/3)`
4. The `Fraction` object will automatically reduce fractions. `(6/4) = (3/2)`

### Trigonometry

You can also do basic trigonometry in Python.

    >>> import math
    >>> math.pi                ①
    3.1415926535897931
    >>> math.sin(math.pi / 2)  ②
    1.0
    >>> math.tan(math.pi / 4)  ③
    0.99999999999999989

1. The `math` module has a constant for π, the ratio of a circle’s circumference to its diameter.
2. The `math` module has all the basic trigonometric functions, including `sin()`, `cos()`, `tan()`, and variants like `asin()`.
3. Note, however, that Python does not have infinite precision. `tan(π / 4)` should return `1.0`, not `0.99999999999999989`.

### Numbers In A Boolean Context

Zero values are false, and non-zero values are true.

You can use numbers in a boolean context, such as an `if` statement. Zero values are false, and non-zero values are true.

    >>> def is_it_true(anything):             ①
    ...   if anything:
    ...     print("yes, it's true")
    ...   else:
    ...     print("no, it's false")
    ...
    >>> is_it_true(1)                         ②
    yes, it's true
    >>> is_it_true(-1)
    yes, it's true
    >>> is_it_true(0)
    no, it's false
    >>> is_it_true(0.1)                       ③
    yes, it's true
    >>> is_it_true(0.0)
    no, it's false
    >>> import fractions
    >>> is_it_true(fractions.Fraction(1, 2))  ④
    yes, it's true
    >>> is_it_true(fractions.Fraction(0, 1))
    no, it's false

1. Did you know you can define your own functions in the Python interactive shell? Just press `ENTER` at the end of each line, and `ENTER` on a blank line to finish.
2. In a boolean context, non-zero integers are true; `0` is false.
3. Non-zero floating point numbers are true; `0.0` is false. Be careful with this one! If there’s the slightest rounding error (not impossible, as you saw in the previous section) then Python will be testing `0.0000000000001` instead of `0` and will return `True`.
4. Fractions can also be used in a boolean context. `Fraction(0, n)` is false for all values of n. All other fractions are true.

## Lists

Lists are Python’s workhorse datatype. When I say “list,” you might be thinking “array whose size I have to declare in advance, that can only contain items of the same type, &c.” Don’t think that. Lists are much cooler than that.

> ☞A list in Python is like an array in Perl 5. In Perl 5, variables that store arrays always start with the `@` character; in Python, variables can be named anything, and Python keeps track of the datatype internally.

> ☞A list in Python is much more than an array in Java (although it can be used as one if that’s really all you want out of life). A better analogy would be to the `ArrayList` class, which can hold arbitrary objects and can expand dynamically as new items are added.

### Creating A List

Creating a list is easy: use square brackets to wrap a comma-separated list of values.

    >>> a_list = ['a', 'b', 'mpilgrim', 'z', 'example']  ①
    >>> a_list
    ['a', 'b', 'mpilgrim', 'z', 'example']
    >>> a_list[0]                                        ②
    'a'
    >>> a_list[4]                                        ③
    'example'
    >>> a_list[-1]                                       ④
    'example'
    >>> a_list[-3]                                       ⑤
    'mpilgrim'

1. First, you define a list of five items. Note that they retain their original order. This is not an accident. A list is an ordered set of items.
2. A list can be used like a zero-based array. The first item of any non-empty list is always `a_list[0]`.
3. The last item of this five-item list is `a_list[4]`, because lists are always zero-based.
4. A negative index accesses items from the end of the list counting backwards. The last item of any non-empty list is always `a_list[-1]`.
5. If the negative index is confusing to you, think of it this way: `a_list[-n] == a_list[len(a_list) - n]`. So in this list, `a_list[-3] == a_list[5 - 3] == a_list[2]`.

### Slicing A List

a_list[0] is the first item of a_list.

Once you’ve defined a list, you can get any part of it as a new list. This is called slicing the list.

    >>> a_list
    ['a', 'b', 'mpilgrim', 'z', 'example']
    >>> a_list[1:3]            ①
    ['b', 'mpilgrim']
    >>> a_list[1:-1]           ②
    ['b', 'mpilgrim', 'z']
    >>> a_list[0:3]            ③
    ['a', 'b', 'mpilgrim']
    >>> a_list[:3]             ④
    ['a', 'b', 'mpilgrim']
    >>> a_list[3:]             ⑤
    ['z', 'example']
    >>> a_list[:]              ⑥
    ['a', 'b', 'mpilgrim', 'z', 'example']

1. You can get a part of a list, called a “slice”, by specifying two indices. The return value is a new list containing all the items of the list, in order, starting with the first slice index (in this case `a_list[1]`), up to but not including the second slice index (in this case `a_list[3]`).
2. Slicing works if one or both of the slice indices is negative. If it helps, you can think of it this way: reading the list from left to right, the first slice index specifies the first item you want, and the second slice index specifies the first item you don’t want. The return value is everything in between.
3. Lists are zero-based, so `a_list[0:3]` returns the first three items of the list, starting at `a_list[0]`, up to but not including `a_list[3]`.
4. If the left slice index is `0`, you can leave it out, and `0` is implied. So `a_list[:3]` is the same as `a_list[0:3]`, because the starting `0` is implied.
5. Similarly, if the right slice index is the length of the list, you can leave it out. So `a_list[3:]` is the same as `a_list[3:5]`, because this list has five items. There is a pleasing symmetry here. In this five-item list, `a_list[:3]` returns the first 3 items, and `a_list[3:]` returns the last two items. In fact, `a_list[:n]` will always return the first n items, and `a_list[n:]` will return the rest, regardless of the length of the list.
6. If both slice indices are left out, all items of the list are included. But this is not the same as the original a_list variable. It is a new list that happens to have all the same items. `a_list[:]` is shorthand for making a complete copy of a list.

### Adding Items To A List

There are four ways to add items to a list.

    >>> a_list = ['a']
    >>> a_list = a_list + [2.0, 3]    ①
    >>> a_list
    ['a', 2.0, 3]
    >>> a_list.append(True)           ②
    >>> a_list
    ['a', 2.0, 3, True]
    >>> a_list.extend(['four', 'e'])  ③
    >>> a_list
    ['a', 2.0, 3, True, 'four', 'e']
    >>> a_list.insert(1, 'a')         ④
    >>> a_list
    ['a', 'a', 2.0, 3, True, 'four', 'e']

1. The `+` operator concatenates lists. A list can contain any number of items; there is no size limit (other than available memory). A list can contain items of any datatype; they don’t all need to be the same type. Here we have a list containing a string, a floating point number, and an integer.
2. The `append()` method adds a single item to the end of the list. (Now we have four different datatypes in the list!)
3. Lists are implemented as classes. “Creating” a list is really instantiating a class. As such, a list has methods that operate on it. The `extend()` method takes one argument, a list, and appends each of the items of the argument to the original list.
4. The `insert()` method inserts a single item into a list. The first argument is the index of the first item in the list that will get bumped out of position. List items do not need to be unique; for example, there are now two separate items with the value `'a'`, `a_list[0]` and `a_list[1]`.

Let’s look closer at the difference between `append()` and `extend()`.

    >>> a_list = ['a', 'b', 'c']
    >>> a_list.extend(['d', 'e', 'f'])  ①
    >>> a_list
    ['a', 'b', 'c', 'd', 'e', 'f']
    >>> len(a_list)                     ②
    6
    >>> a_list[-1]
    'f'
    >>> a_list.append(['g', 'h', 'i'])  ③
    >>> a_list
    ['a', 'b', 'c', 'd', 'e', 'f', ['g', 'h', 'i']]
    >>> len(a_list)                     ④
    7
    >>> a_list[-1]
    ['g', 'h', 'i']

1. The `extend()` method takes a single argument, which is always a list, and adds each of the items of that list to a_list.
2. If you start with a list of three items and extend it with a list of another three items, you end up with a list of six items.
3. On the other hand, the `append()` method takes any number of arguments, each of which can be any datatype. Here, you’re calling the `append()` method with a single argument, a list of three items.
4. If you start with a list of six items and append a list onto it, you end up with... a list of seven items. Why seven? Because the last item (which you just appended) is itself a list. Lists can contain any type of data, including other lists. That may be what you want, or it may not. But it’s what you asked for, and it’s what you got.

### Searching For Values In A List

    >>> a_list = ['a', 'b', 'new', 'mpilgrim', 'new']
    >>> 'mpilgrim' in a_list      ①
    True
    >>> a_list.index('mpilgrim')  ②
    3
    >>> a_list.index('new')       ③
    2
    >>> 'c' in a_list             ④
    False
    >>> a_list.index('c')         ⑤
    Traceback (innermost last):
      File "<interactive input>", line 1, in ?
    ValueError: list.index(x): x not in list

1. To test whether a value is in the list, use the `in` operator. It returns `True` if the value is in the list, or `False` if it is not. It will not tell you where in the list the value is.
2. If you need to know exactly where in the list a value is, call the `index()` method. By default it will search the entire list, although you can specify a second argument of the (`0`-based) index to start from, and even a third argument of the (`0`-based) index to stop searching.
3. As you might expect, this will return `False`, because `'c'` is not a value in a_list.
4. The `index()` method finds the first occurrence of a value in the list. In this case, `'new'` occurs twice in the list, in `a_list[2]` and `a_list[4]`, but the `index()` method will return only the index of the first occurrence.
5. As you might not expect, if the value is not found in the list, Python raises an exception. This is notably different from most languages, which will return some invalid index (like `-1`). While this may seem annoying at first, I think you will come to appreciate it. It means your program will crash at the source of the problem instead of failing strangely and silently later.

### Lists In A Boolean Context

Empty lists are false; all other lists are true.

You can also use a list in a boolean context, such as an `if` statement.

    >>> def is_it_true(anything):
    ...   if anything:
    ...     print("yes, it's true")
    ...   else:
    ...     print("no, it's false")
    ...
    >>> is_it_true([])             ②
    no, it's false
    >>> is_it_true(['a'])          ③
    yes, it's true

1. In a boolean context, an empty list is false.
2. Any list with at least one item is true.

## Dictionaries

One of Python’s most important datatypes is the dictionary, which defines one-to-one relationships between keys and values.

> ☞A dictionary in Python is like a hash in Perl 5. In Perl 5, variables that store hashes always start with a `%` character. In Python, variables can be named anything, and Python keeps track of the datatype internally.

### Creating A Dictionary

Creating a dictionary is easy. The syntax is similar to sets, but instead of values, you have key-value pairs. Once you have a dictionary, you can look up values by their key.

    >>> a_dict = {"server":"db.diveintopython3.org", "database":"mysql"}  ①
    >>> a_dict
    {'server': 'db.diveintopython3.org', 'database': 'mysql'}
    >>> a_dict["server"]                                                  ②
    'db.diveintopython3.org'
    >>> a_dict["database"]                                                ③
    'mysql'
    >>> a_dict["db.diveintopython3.org"]                                  ④
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    KeyError: 'db.diveintopython3.org'

1. First, you create a new dictionary with two items and assign it to the variable a_dict. Each item is a key-value pair, and the whole set of items is enclosed in curly braces.
2. `'server'` is a key, and its associated value, referenced by `a_dict["server"]`, is `'db.diveintopython3.org'`.
3. `'database'` is a key, and its associated value, referenced by `a_dict["database"]`, is `'mysql'`.
4. You can get values by key, but you can’t get keys by value. So `a_dict["server"]` is `'db.diveintopython3.org'`, but `a_dict["db.diveintopython3.org"]` raises an exception, because `'db.diveintopython3.org'` is not a key.

### Modifying A Dictionary

Dictionaries do not have any predefined size limit. You can add new key-value pairs to a dictionary at any time, or you can modify the value of an existing key. Continuing from the previous example:

    >>> a_dict
    {'server': 'db.diveintopython3.org', 'database': 'mysql'}
    >>> a_dict["database"] = "blog"  ①
    >>> a_dict
    {'server': 'db.diveintopython3.org', 'database': 'blog'}
    >>> a_dict["user"] = "mark"      ②
    >>> a_dict                       ③
    {'server': 'db.diveintopython3.org', 'user': 'mark', 'database': 'blog'}
    >>> a_dict["user"] = "dora"      ④
    >>> a_dict
    {'server': 'db.diveintopython3.org', 'user': 'dora', 'database': 'blog'}
    >>> a_dict["User"] = "mark"      ⑤
    >>> a_dict
    {'User': 'mark', 'server': 'db.diveintopython3.org', 'user': 'dora', 'database': 'blog'}

1. You can not have duplicate keys in a dictionary. Assigning a value to an existing key will wipe out the old value.
2. You can add new key-value pairs at any time. This syntax is identical to modifying existing values.
3. The new dictionary item (key `'user'`, value `'mark'`) appears to be in the middle. In fact, it was just a coincidence that the items appeared to be in order in the first example; it is just as much a coincidence that they appear to be out of order now.
4. Assigning a value to an existing dictionary key simply replaces the old value with the new one.
5. Will this change the value of the `user` key back to "mark"? No! Look at the key closely — that’s a capital `U` in `"User"`. Dictionary keys are case-sensitive, so this statement is creating a new key-value pair, not overwriting an existing one. It may look similar to you, but as far as Python is concerned, it’s completely different.

### Mixed-Value Dictionaries

Dictionaries aren’t just for strings. Dictionary values can be any datatype, including integers, booleans, arbitrary objects, or even other dictionaries. And within a single dictionary, the values don’t all need to be the same type; you can mix and match as needed. Dictionary keys are more restricted, but they can be strings, integers, and a few other types. You can also mix and match key datatypes within a dictionary.

In fact, you’ve already seen a dictionary with non-string keys and values, in your first Python program.

    SUFFIXES = {1000: ('KB', 'MB', 'GB', 'TB', 'PB', 'EB', 'ZB', 'YB'),
                1024: ('KiB', 'MiB', 'GiB', 'TiB', 'PiB', 'EiB', 'ZiB', 'YiB')}

Let's tear that apart in the interactive shell.

    >>> SUFFIXES = {1000: ['KB', 'MB', 'GB', 'TB', 'PB', 'EB', 'ZB', 'YB'],
    ...             1024: ['KiB', 'MiB', 'GiB', 'TiB', 'PiB', 'EiB', 'ZiB', 'YiB']}
    >>> len(SUFFIXES)      ①
    2
    >>> SUFFIXES[1000]     ②
    ['KB', 'MB', 'GB', 'TB', 'PB', 'EB', 'ZB', 'YB']
    >>> SUFFIXES[1024]     ③
    ['KiB', 'MiB', 'GiB', 'TiB', 'PiB', 'EiB', 'ZiB', 'YiB']
    >>> SUFFIXES[1000][3]  ④
    'TB'

1. As with lists, the `len()` function gives you the number of items in a dictionary.
2. `1000` is a key in the `SUFFIXES` dictionary; its value is a list of eight items (eight strings, to be precise).
3. Similarly, `1024` is a key in the `SUFFIXES` dictionary; its value is also a list of eight items.
4. Since `SUFFIXES[1000]` is a list, you can address individual items in the list by their 0-based index.

### Dictionaries In A Boolean Context

Empty dictionaries are false; all other dictionaries are true.

You can also use a dictionary in a boolean context, such as an `if` statement.

    >>> def is_it_true(anything):
    ...   if anything:
    ...     print("yes, it's true")
    ...   else:
    ...     print("no, it's false")
    ...
    >>> is_it_true({})             ①
    no, it's false
    >>> is_it_true({'a': 1})       ②
    yes, it's true

1. In a boolean context, an empty dictionary is false.
2. Any dictionary with at least one key-value pair is true.

## `None`

`None` is a special constant in Python. It is a null value. `None` is not the same as `False`. `None` is not `0`. `None` is not an empty string. Comparing `None` to anything other than `None` will always return `False`.

`None` is the only null value. It has its own datatype (`NoneType`). You can assign `None` to any variable, but you can not create other `NoneType` objects. All variables whose value is `None` are equal to each other.

    >>> type(None)
    <class 'NoneType'>
    >>> None == False
    False
    >>> None == 0
    False
    >>> None == ''
    False
    >>> None == None
    True
    >>> x = None
    >>> x == None
    True
    >>> y = None
    >>> x == y
    True

### `None` In A Boolean Context

In a boolean context, `None` is false and `not None` is true.

    >>> def is_it_true(anything):
    ...   if anything:
    ...     print("yes, it's true")
    ...   else:
    ...     print("no, it's false")
    ...
    >>> is_it_true(None)
    no, it's false
    >>> is_it_true(not None)
    yes, it's true

## Further Reading

- The `fractions` module
- The `math` module
- PEP 237: Unifying Long Integers and Integers
- PEP 238: Changing the Division Operator

© 2001–9 Mark Pilgrim