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Python Reference Manual |  |
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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:
| m_expr | ::= | u_expr | m_expr "*" u_expr | m_expr "//" u_expr | m_expr "/" u_expr |
| m_expr "%" u_expr | ||
| a_expr | ::= | m_expr | a_expr "+" m_expr | a_expr "-" m_expr |
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 operand5.2.
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) - 15.3.
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.
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.
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.
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Python Reference Manual | |
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