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<H1><A NAME="SECTION007600000000000000000"> </A>
<BR>
5.6 Binary arithmetic operations
</H1>
<a name="l2h-272"> </a>
<P>
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:
<P>
<dl><dd class="grammar">
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<table cellpadding="2">
<tr valign="baseline">
<td><code><a name="tok-m_expr">m_expr</a></code></td>
<td> ::= </td>
<td><code><a href="unary.html#tok-u_expr">u_expr</a> | <a href="node57.html#tok-m_expr">m_expr</a> "*" <a href="unary.html#tok-u_expr">u_expr</a>
| <a href="node57.html#tok-m_expr">m_expr</a> "/" <a href="unary.html#tok-u_expr">u_expr</a>
| <a href="node57.html#tok-m_expr">m_expr</a> "%" <a href="unary.html#tok-u_expr">u_expr</a></code></td></tr>
<tr valign="baseline">
<td><code><a name="tok-a_expr">a_expr</a></code></td>
<td> ::= </td>
<td><code><a href="binary.html#tok-m_expr">m_expr</a> | <a href="">aexpr</a> "+" <a href="binary.html#tok-m_expr">m_expr</a>
<a href="">aexpr</a> "-" <a href="binary.html#tok-m_expr">m_expr</a></code></td></tr>
</table>
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<a class="grammar-footer"
href="grammar.txt" type="text/plain"
>Download entire grammar as text.</a>
</dd></dl>
<P>
The <code>*</code> (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.
<a name="l2h-273"> </a>
<P>
The <code>/</code> (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
<tt class="exception">ZeroDivisionError</tt> exception.
<a name="l2h-274"> </a>
<P>
The <code>%</code> (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 <tt class="exception">ZeroDivisionError</tt> exception. The arguments may be floating
point numbers, e.g., <code>3.14%0.7</code> equals <code>0.34</code> (since
<code>3.14</code> equals <code>4*0.7 + 0.34</code>.) 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.
<a name="l2h-275"> </a>
<P>
The integer division and modulo operators are connected by the
following identity: <code>x == (x/y)*y + (x%y)</code>. Integer division and
modulo are also connected with the built-in function <tt class="function">divmod()</tt>:
<code>divmod(x, y) == (x/y, x%y)</code>. These identities don't hold for
floating point and complex numbers; there similar identities hold
approximately where <code>x/y</code> is replaced by <code>floor(x/y)</code>) or
<code>floor(x/y) - 1</code> (for floats),<A NAME="tex2html4"
HREF="#foot3686"><SUP>5.2</SUP></A> or <code>floor((x/y).real)</code> (for
complex).
<P>
The <code>+</code> (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.
<a name="l2h-276"> </a>
<P>
The <code>-</code> (subtraction) operator yields the difference of its
arguments. The numeric arguments are first converted to a common
type.
<a name="l2h-277"> </a>
<P>
<BR><HR><H4>Footnotes</H4>
<DL>
<DT><A NAME="foot3686">... floats),</A><A NAME="foot3686"
href="binary.html#tex2html4"><SUP>5.2</SUP></A>
<DD>
If x is very close to an exact integer multiple of y, it's
possible for <code>floor(x/y)</code> to be one larger than
<code>(x-x%y)/y</code> due to rounding. In such cases, Python returns
the latter result, in order to preserve that <code>divmod(x,y)[0]
* y + x % y</code> be very close to <code>x</code>.
</DL>
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<span class="release-info">Release 2.2, documentation updated on December 21, 2001.</span>
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