Python Expression Operators

Perhaps the most fundamental tool that processes numbers is the expression: a combination of numbers (or other objects) and operators that computes a value when executed by Python. In Python, expressions are written using the usual mathematical notation and operator symbols. For instance, to add two numbers X and Y you would say X + Y, which tells Python to apply the + operator to the values named by X and Y. The result of the expression is the sum of X and Y, another number object.

Table 5-2 lists all the operator expressions available in Python. Many are self-explanatory; for instance, the usual mathematical operators (+, −, *, /, and so on) are supported. A few will be familiar if you’ve used other languages in the past: % computes a division remainder, << performs a bitwise left-shift, & computes a bitwise AND result, and so on. Others are more Python-specific, and not all are numeric in nature: for example, the is operator tests object identity (i.e., address in memory, a strict form of equality), and lambda creates unnamed functions.

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Table 5-2. Python expression operators and precedence

Operators

Description

yield x

Generator function send protocol

lambda args: expression

Anonymous function generation

x if y else z

Ternary selection (x is evaluated only if y is true)

x or y

Logical OR (y is evaluated only if x is false)

x and y

Logical AND (y is evaluated only if x is true)

not x

Logical negation

x in y, x not in y

Membership (iterables, sets)

x is y, x is not y

Object identity tests

x < y, x <= y, x > y, x >= y

x == y, x != y

Magnitude comparison, set subset and superset;

Value equality operators

x | y

Bitwise OR, set union

x ^ y

Bitwise XOR, set symmetric difference

x & y

Bitwise AND, set intersection

x << y, x >> y

Shift x left or right by y bits

x + y

x – y

Addition, concatenation;

Subtraction, set difference

x * y

x % y

x / y, x // y

Multiplication, repetition;

Remainder, format;

Division: true and floor

−x, +x

Negation, identity

˜x

Bitwise NOT (inversion)

x ** y

Power (exponentiation)

x[i]

Indexing (sequence, mapping, others)

x[i:j:k]

Slicing

x(...)

Call (function, method, class, other callable)

x.attr

Attribute reference

(...)

Tuple, expression, generator expression

[...]

List, list comprehension

{...}

Dictionary, set, set and dictionary comprehensions

Since this book addresses both Python 2.6 and 3.0, here are some notes about version differences and recent additions related to the operators in Table 5-2:

 

 
  • In Python 2.6, value inequality can be written as either X != Y or X <> Y. In Python 3.0, the latter of these options is removed because it is redundant. In either version, best practice is to use X != Y for all value inequality tests.
  • In Python 2.6, a backquotes expression `X` works the same as repr(X) and converts objects to display strings. Due to its obscurity, this expression is removed in Python 3.0; use the more readable str and repr built-in functions, described in Numeric Display Formats.
  • The X // Y floor division expression always truncates fractional remainders in both Python 2.6 and 3.0. The X / Y expression performs true division in 3.0 (retaining remainders) and classic division in 2.6 (truncating for integers). See Division: Classic, Floor, and True.
  • The syntax [...] is used for both list literals and list comprehension expressions. The latter of these performs an implied loop and collects expression results in a new list. See Chapters 4, 14, and 20 for examples.
  • The syntax (...) is used for tuples and expressions, as well as generator expressions—a form of list comprehension that produces results on demand, instead of building a result list. See Chapters 4 and 20 for examples. The parentheses may sometimes be omitted in all three constructs.
  • The syntax {...} is used for dictionary literals, and in Python 3.0 for set literals and both dictionary and set comprehensions. See the set coverage in this chapter and Chapters 4, 8, 14, and 20 for examples.
  • The yield and ternary if/else selection expressions are available in Python 2.5 and later. The former returns send(...) arguments in generators; the latter is shorthand for a multiline if statement. yield requires parentheses if not alone on the right side of an assignment statement.
  • Comparison operators may be chained: X < Y < Z produces the same result as X < Y and Y < Z. See Comparisons: Normal and Chained for details.
  • In recent Pythons, the slice expression X[I:J:K] is equivalent to indexing with a slice object: X[slice(I, J, K)].
  • In Python 2.X, magnitude comparisons of mixed types—converting numbers to a common type, and ordering other mixed types according to the type name—are allowed. In Python 3.0, nonnumeric mixed-type magnitude comparisons are not allowed and raise exceptions; this includes sorts by proxy.
  • Magnitude comparisons for dictionaries are also no longer supported in Python 3.0 (though equality tests are); comparing sorted(dict.items()) is one possible replacement.

We’ll see most of the operators in Table 5-2 in action later; first, though, we need to take a quick look at the ways these operators may be combined in expressions.

Mixed operators follow operator precedence

As in most languages, in Python, more complex expressions are coded by stringing together the operator expressions in Table 5-2. For instance, the sum of two multiplications might be written as a mix of variables and operators:

A * B + C * D

So, how does Python know which operation to perform first? The answer to this question lies in operator precedence. When you write an expression with more than one operator, Python groups its parts according to what are called precedence rules, and this grouping determines the order in which the expression’s parts are computed. Table 5-2 is ordered by operator precedence:

 

 
  • Operators lower in the table have higher precedence, and so bind more tightly in mixed expressions.
  • Operators in the same row in Table 5-2 generally group from left to right when combined (except for exponentiation, which groups right to left, and comparisons, which chain left to right).

For example, if you write X + Y * Z, Python evaluates the multiplication first (Y * Z), then adds that result to X because * has higher precedence (is lower in the table) than +. Similarly, in this section’s original example, both multiplications (A * B and C * D) will happen before their results are added.

Parentheses group subexpressions

You can forget about precedence completely if you’re careful to group parts of expressions with parentheses. When you enclose subexpressions in parentheses, you override Python’s precedence rules; Python always evaluates expressions in parentheses first before using their results in the enclosing expressions.

For instance, instead of coding X + Y * Z, you could write one of the following to force Python to evaluate the expression in the desired order:

(X + Y) * Z
X + (Y * Z)

In the first case, + is applied to X and Y first, because this subexpression is wrapped in parentheses. In the second case, the * is performed first (just as if there were no parentheses at all). Generally speaking, adding parentheses in large expressions is a good idea—it not only forces the evaluation order you want, but also aids readability.

Mixed types are converted up

Besides mixing operators in expressions, you can also mix numeric types. For instance, you can add an integer to a floating-point number:

40 + 3.14

But this leads to another question: what type is the result—integer or floating-point? The answer is simple, especially if you’ve used almost any other language before: in mixed-type numeric expressions, Python first converts operands up to the type of the most complicated operand, and then performs the math on same-type operands. This behavior is similar to type conversions in the C language.

Python ranks the complexity of numeric types like so: integers are simpler than floating-point numbers, which are simpler than complex numbers. So, when an integer is mixed with a floating point, as in the preceding example, the integer is converted up to a floating-point value first, and floating-point math yields the floating-point result. Similarly, any mixed-type expression where one operand is a complex number results in the other operand being converted up to a complex number, and the expression yields a complex result. (In Python 2.6, normal integers are also converted to long integers whenever their values are too large to fit in a normal integer; in 3.0, integers subsume longs entirely.)

You can force the issue by calling built-in functions to convert types manually:

>>> int(3.1415)     # Truncates float to integer
3
>>> float(3)        # Converts integer to float
3.0

However, you won’t usually need to do this: because Python automatically converts up to the more complex type within an expression, the results are normally what you want.

Also, keep in mind that all these mixed-type conversions apply only when mixing numeric types (e.g., an integer and a floating-point) in an expression, including those using numeric and comparison operators. In general, Python does not convert across any other type boundaries automatically. Adding a string to an integer, for example, results in an error, unless you manually convert one or the other; watch for an example when we meet strings in Chapter 7.

Note

In Python 2.6, nonnumeric mixed types can be compared, but no conversions are performed (mixed types compare according to a fixed but arbitrary rule). In 3.0, nonnumeric mixed-type comparisons are not allowed and raise exceptions.

Preview: Operator overloading and polymorphism

Although we’re focusing on built-in numbers right now, all Python operators may be overloaded (i.e., implemented) by Python classes and C extension types to work on objects you create. For instance, you’ll see later that objects coded with classes may be added or concatenated with + expressions, indexed with [i] expressions, and so on.

Furthermore, Python itself automatically overloads some operators, such that they perform different actions depending on the type of built-in objects being processed. For example, the + operator performs addition when applied to numbers but performs concatenation when applied to sequence objects such as strings and lists. In fact, + can mean anything at all when applied to objects you define with classes.

As we saw in the prior chapter, this property is usually called polymorphism—a term indicating that the meaning of an operation depends on the type of the objects being operated on. We’ll revisit this concept when we explore functions in Chapter 16, because it becomes a much more obvious feature in that context.