Python
supplies the usual numeric operations, as you’ve
just seen in Table 4-2. All numbers are immutable
objects, so when you perform a numeric operation on a number object,
you always produce a new number object. You can access the parts of a
complex object `z`

as read-only attributes
`z.real`

and `z.imag`

. Trying to
rebind these attributes on a complex object raises an exception.

Note that a number’s optional `+`

or `-`

sign, and the `+`

that joins
a floating-point literal to an imaginary one to make a complex
number, are not part of the literals’ syntax. They
are ordinary operators, subject to normal operator precedence rules
(see Table 4-2). This is why, for example,
`-2**2`

evaluates to `-4`

:
exponentiation has higher precedence than unary minus, so the whole
expression parses as `-(2**2)`

, not as
`(-2)**2`

.

You can perform arithmetic
operations and comparisons between any two numbers. If the
operands’ types differ,
`coercion`

applies: Python converts the operand
with the smaller type to the larger type. The types, in order from
smallest to largest, are integers, long integers, floating-point
numbers, and complex numbers.

You can also perform an explicit conversion by passing a numeric
argument to any of the built-ins: `int`

,
`long`

, `float`

, and
`complex`

. `int`

and
`long`

drop their argument’s
fractional part, if any (e.g., `int(9.8)`

is
`9`

). Converting from a complex number to any other
numeric type drops the imaginary part. You can also call
`complex`

with two arguments, giving real and
imaginary parts.

Each built-in type can also take a string argument with the syntax of
an appropriate numeric literal with two small extensions: the
argument string may start with a sign and, for complex numbers, may
sum or subtract real and imaginary parts. `int`

and
`long`

can also be called with two arguments: the
first one a string to convert, and the second one the
*radix*, an integer between 2 and 36 to use as the
base for the conversion (e.g., `int('101',2)`

returns `5`

, the value of '`101`

'
in base `2`

).

If the right operand of
`/`

, `//`

, or `%`

is `0`

, Python raises a runtime exception. The
`//`

operator, introduced in Python 2.2, performs
truncating division, which means it returns an integer result
(converted to the same type as the wider operand) and ignores the
remainder, if any. When both operands are integers, the
`/`

operator behaves like `//`

if
you are using Python 2.1 and earlier or if the switch
`-Qold`

was used on the Python command line
(`-Qold`

is the default in Python 2.2). Otherwise,
`/`

performs true division, returning a
floating-point result (or a complex result, if either operand is a
complex number). To have `/`

perform true division
on integer operands in Python 2.2, use the switch
`-Qnew`

on the Python command line or begin your
source file with the statement:

from __future__ import division

This ensures that operator `/`

works without
truncation on any type of operands.

To ensure that your program’s behavior does not
depend on the `-Q`

switch, use `//`

(in Python 2.2 and later) to get truncating division. When you do not
want truncation, ensure that at least one operand is not an integer.
For example, instead of `a/b`

, use
`1.*a/b`

to avoid making any assumption on the types
of `a`

and `b`

. To check whether
your program has version dependencies in its use of division, use the
switch `-Qwarn`

on the Python command line (in
Python 2.2 and later) to get warnings about uses of
`/`

on integer operands.

The built-in `divmod`

function takes two numeric
arguments and returns a pair whose items are the quotient and
remainder, thus saving you from having to use both
`//`

for the quotient and `%`

for
the remainder.

An exponentiation operation,
`a`

`**`

* b*,
raises an exception if

*is less than zero and*

`a`

*is a floating-point value with a non-zero fractional part. The built-in*

`b`

`pow(`

*,*

`a`

`b`

`)`

function returns the same result as

`a`

`**`

*. With three arguments,*

`b`

`pow(`

*,*

`a`

*,*

`b`

`c`

`)`

returns the same result as
`(`

`a`

`**`

`b`

`)%`

*, but faster.*

`c`

All
objects, including numbers, can also be compared for equality
(`= =`

) and inequality (`!=`

).
Comparisons requiring order (`<`

,
`<=`

, `>`

,
`>=`

) may be used between any two numbers except
complex ones, for which they raise runtime exceptions. All these
operators return Boolean values (`True`

or
`False`

).

Integers and long
integers can be considered strings of bits and used with the bitwise
operations shown in Table 4-2. Bitwise operators
have lower priority than arithmetic operators. Positive integers are
extended by an infinite string of `0`

bits on the
left. Negative integers are represented in two’s
complement notation, and therefore are extended by an infinite string
of `1`

bits on the left.

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