5.6 Binary arithmetic operations

The binary arithmetic operations have the conventional priority levels. Note that some of these operations also apply to certain non-numeric types. Apart from the power operator, there are only two levels, one for multiplicative operators and one for additive operators:

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The `*`

(multiplication) operator yields the product of its
arguments. The arguments must either both be numbers, or one argument
must be an integer (plain or long) and the other must be a sequence.
In the former case, the numbers are converted to a common type and
then multiplied together. In the latter case, sequence repetition is
performed; a negative repetition factor yields an empty sequence.

The `/`

(division) and `//`

(floor division) operators yield
the quotient of their arguments. The numeric arguments are first
converted to a common type. Plain or long integer division yields an
integer of the same type; the result is that of mathematical division
with the `floor' function applied to the result. Division by zero
raises the
`ZeroDivisionError` exception.

The `%`

(modulo) operator yields the remainder from the
division of the first argument by the second. The numeric arguments
are first converted to a common type. A zero right argument raises
the `ZeroDivisionError` exception. The arguments may be floating
point numbers, e.g., `3.14%0.7`

equals `0.34`

(since
`3.14`

equals `4*0.7 + 0.34`

.) The modulo operator always
yields a result with the same sign as its second operand (or zero);
the absolute value of the result is strictly smaller than the absolute
value of the second operand^{5.2}.

The integer division and modulo operators are connected by the
following identity: `x == (x/y)*y + (x%y)`

. Integer division and
modulo are also connected with the built-in function `divmod()`:
`divmod(x, y) == (x/y, x%y)`

. These identities don't hold for
floating point numbers; there similar identities hold
approximately where `x/y`

is replaced by `floor(x/y)`

or
`floor(x/y) - 1`

^{5.3}.

In addition to performing the modulo operation on numbers, the `%`

operator is also overloaded by string and unicode objects to perform
string formatting (also known as interpolation). The syntax for string
formatting is described in the
*Python Library Reference*,
section ``Sequence Types''.

The `+`

(addition) operator yields the sum of its arguments.
The arguments must either both be numbers or both sequences of the
same type. In the former case, the numbers are converted to a common
type and then added together. In the latter case, the sequences are
concatenated.

The `-`

(subtraction) operator yields the difference of its
arguments. The numeric arguments are first converted to a common
type.

- ... operand
^{5.2} -
While
`abs(x%y) < abs(y)`

is true mathematically, for floats it may not be true numerically due to roundoff. For example, and assuming a platform on which a Python float is an IEEE 754 double-precision number, in order that`-1e-100 % 1e100`

have the same sign as`1e100`

, the computed result is`-1e-100 + 1e100`

, which is numerically exactly equal to`1e100`

. Function`fmod()`in the`math`module returns a result whose sign matches the sign of the first argument instead, and so returns`-1e-100`

in this case. Which approach is more appropriate depends on the application. - ... 1
^{5.3} -
If x is very close to an exact integer multiple of y, it's
possible for
`floor(x/y)`

to be one larger than`(x-x%y)/y`

due to rounding. In such cases, Python returns the latter result, in order to preserve that`divmod(x,y)[0] * y + x % y`

be very close to`x`

.