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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:

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

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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^5.1.

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) - 1^5.2.

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.

Footnotes

... operand^5.1

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.

... 1^5.2

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.

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