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<title>5.6 Binary arithmetic operations</title>
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<H1><A NAME="SECTION007600000000000000000"></A><A NAME="binary"></A>
<BR>
5.6 Binary arithmetic operations
</H1>
<a id='l2h-414' xml:id='l2h-414'></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">
<div class="productions">
<table>
<tr>
    <td><a id='tok-m_expr' xml:id='tok-m_expr'>m_expr</a></td>
    <td>::=</td>
    <td><a class='grammartoken' href="unary.html#tok-u_expr">u_expr</a> | <a class='grammartoken' href="binary.html#tok-m_expr">m_expr</a> "*" <a class='grammartoken' href="unary.html#tok-u_expr">u_expr</a>
              | <a class='grammartoken' href="binary.html#tok-m_expr">m_expr</a> "//" <a class='grammartoken' href="unary.html#tok-u_expr">u_expr</a>
              | <a class='grammartoken' href="binary.html#tok-m_expr">m_expr</a> "/" <a class='grammartoken' href="unary.html#tok-u_expr">u_expr</a></td></tr>
  <tr>
    <td></td>
    <td></td>
    <td><code>| <a class='grammartoken' href="binary.html#tok-m_expr">m_expr</a> "%" <a class='grammartoken' href="unary.html#tok-u_expr">u_expr</a></code></td></tr>
  <tr>
    <td><a id='tok-a_expr' xml:id='tok-a_expr'>a_expr</a></td>
    <td>::=</td>
    <td><a class='grammartoken' href="binary.html#tok-m_expr">m_expr</a> | <a class='grammartoken' href="binary.html#tok-a_expr">a_expr</a> "+" <a class='grammartoken' href="binary.html#tok-m_expr">m_expr</a>
              | <a class='grammartoken' href="binary.html#tok-a_expr">a_expr</a> "-" <a class='grammartoken' href="binary.html#tok-m_expr">m_expr</a></td></tr>
</table>
</div>
<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 id='l2h-416' xml:id='l2h-416'></a>

<P>
The <code>/</code> (division) and <code>//</code> (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
<tt class="exception">ZeroDivisionError</tt> exception.
<a id='l2h-415' xml:id='l2h-415'></a><a id='l2h-417' xml:id='l2h-417'></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 absolute
value of the second operand<A NAME="tex2html5"
  HREF="#foot4570"><SUP>5.2</SUP></A>.
<a id='l2h-418' xml:id='l2h-418'></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 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><A NAME="tex2html6"
  HREF="#foot4636"><SUP>5.3</SUP></A>.

<P>
<div class="versionnote"><b>Deprecated since release 2.3.</b>
The floor division operator, the modulo operator,
and the <tt class="function">divmod()</tt> function are no longer defined for complex
numbers.  Instead, convert to a floating point number using the
<tt class="function">abs()</tt> function if appropriate.</div><p></p>

<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 id='l2h-419' xml:id='l2h-419'></a>

<P>
The <code>-</code> (subtraction) operator yields the difference of its
arguments.  The numeric arguments are first converted to a common
type.
<a id='l2h-420' xml:id='l2h-420'></a>

<P>
<BR><HR><H4>Footnotes</H4>
<DL>
<DT><A NAME="foot4570">... operand</A><A
 href="binary.html#tex2html5"><SUP>5.2</SUP></A></DT>
<DD>
    While <code>abs(x%y) &lt; abs(y)</code> 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 <code>-1e-100 % 1e100</code>
    have the same sign as <code>1e100</code>, the computed result is
    <code>-1e-100 + 1e100</code>, which is numerically exactly equal
    to <code>1e100</code>.  Function <tt class="function">fmod()</tt> in the <tt class="module">math</tt>
    module returns a result whose sign matches the sign of the
    first argument instead, and so returns <code>-1e-100</code> in this case.
    Which approach is more appropriate depends on the application.


</DD>
<DT><A NAME="foot4636">... 1</A><A
 href="binary.html#tex2html6"><SUP>5.3</SUP></A></DT>
<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>.


</DD>
</DL>
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<span class="release-info">Release 2.4.2, documentation updated on 28 September 2005.</span>
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