5.6 Binary arithmetic operations
Keywords: ref

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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
      a_expr:         m_expr | aexpr "+" m_expr | aexpr "-" m_expr

The `*` (multiplication) operator yields the product of its arguments. The arguments must either both be numbers, or one argument must be a plain integer 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) operator yields the quotient of its 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 second operand.

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 and complex numbers; there similar identities hold approximately where `x/y` is replaced by `floor(x/y)`) or `floor(x/y) - 1` (for floats),5.1 or `floor((x/y).real)` (for complex).

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

... floats),5.1
  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`.