[OpenSPARC-T2-SAM] / sam-t2 / devtools / v9 / html / python / ref / binary.html

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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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	45	<a class="sectref" rel="prev" href="unary.html">5.5 Unary arithmetic operations</A>
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	54
	55	<H1><A NAME="SECTION007600000000000000000"></A><A NAME="binary"></A>
	56	<BR>
	57	5.6 Binary arithmetic operations
	58	</H1>
	59	<a id='l2h-414' xml:id='l2h-414'></a>
	60	<P>
	61	The binary arithmetic operations have the conventional priority
	62	levels. Note that some of these operations also apply to certain
	63	non-numeric types. Apart from the power operator, there are only two
	64	levels, one for multiplicative operators and one for additive
65	operators:
66
67	<P>
68	<dl><dd class="grammar">
69	<div class="productions">
70	<table>
71	<tr>
72	<td><a id='tok-m_expr' xml:id='tok-m_expr'>m_expr</a></td>
73	<td>::=</td>
74	<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>
75	\| <a class='grammartoken' href="binary.html#tok-m_expr">m_expr</a> "//" <a class='grammartoken' href="unary.html#tok-u_expr">u_expr</a>
76	\| <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>
77	<tr>
78	<td></td>
79	<td></td>
80	<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>
81	<tr>
82	<td><a id='tok-a_expr' xml:id='tok-a_expr'>a_expr</a></td>
83	<td>::=</td>
84	<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>
85	\| <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>
86	</table>
87	</div>
88	<a class="grammar-footer"
89	href="grammar.txt" type="text/plain"
90	>Download entire grammar as text.</a>
91	</dd></dl>
92
93	<P>
94	The <code>*</code> (multiplication) operator yields the product of its
95	arguments. The arguments must either both be numbers, or one argument
96	must be an integer (plain or long) and the other must be a sequence.
97	In the former case, the numbers are converted to a common type and
98	then multiplied together. In the latter case, sequence repetition is
99	performed; a negative repetition factor yields an empty sequence.
100	<a id='l2h-416' xml:id='l2h-416'></a>
101
102	<P>
103	The <code>/</code> (division) and <code>//</code> (floor division) operators yield
104	the quotient of their arguments. The numeric arguments are first
105	converted to a common type. Plain or long integer division yields an
106	integer of the same type; the result is that of mathematical division
107	with the `floor' function applied to the result. Division by zero
108	raises the
109	<tt class="exception">ZeroDivisionError</tt> exception.
110	<a id='l2h-415' xml:id='l2h-415'></a><a id='l2h-417' xml:id='l2h-417'></a>
111
112	<P>
113	The <code>%</code> (modulo) operator yields the remainder from the
114	division of the first argument by the second. The numeric arguments
115	are first converted to a common type. A zero right argument raises
116	the <tt class="exception">ZeroDivisionError</tt> exception. The arguments may be floating
117	point numbers, e.g., <code>3.14%0.7</code> equals <code>0.34</code> (since
118	<code>3.14</code> equals <code>4*0.7 + 0.34</code>.) The modulo operator always
119	yields a result with the same sign as its second operand (or zero);
120	the absolute value of the result is strictly smaller than the absolute
121	value of the second operand<A NAME="tex2html5"
122	HREF="#foot4570"><SUP>5.2</SUP></A>.
123	<a id='l2h-418' xml:id='l2h-418'></a>
124
125	<P>
126	The integer division and modulo operators are connected by the
127	following identity: <code>x == (x/y)*y + (x%y)</code>. Integer division and
128	modulo are also connected with the built-in function <tt class="function">divmod()</tt>:
129	<code>divmod(x, y) == (x/y, x%y)</code>. These identities don't hold for
130	floating point numbers; there similar identities hold
131	approximately where <code>x/y</code> is replaced by <code>floor(x/y)</code> or
132	<code>floor(x/y) - 1</code><A NAME="tex2html6"
133	HREF="#foot4636"><SUP>5.3</SUP></A>.
134
135	<P>
136	<div class="versionnote"><b>Deprecated since release 2.3.</b>
137	The floor division operator, the modulo operator,
138	and the <tt class="function">divmod()</tt> function are no longer defined for complex
139	numbers. Instead, convert to a floating point number using the
140	<tt class="function">abs()</tt> function if appropriate.</div><p></p>
141
142	<P>
143	The <code>+</code> (addition) operator yields the sum of its arguments.
144	The arguments must either both be numbers or both sequences of the
145	same type. In the former case, the numbers are converted to a common
146	type and then added together. In the latter case, the sequences are
147	concatenated.
148	<a id='l2h-419' xml:id='l2h-419'></a>
149
150	<P>
151	The <code>-</code> (subtraction) operator yields the difference of its
152	arguments. The numeric arguments are first converted to a common
153	type.
154	<a id='l2h-420' xml:id='l2h-420'></a>
155
156	<P>
157	<BR><HR><H4>Footnotes</H4>
158	<DL>
159	<DT><A NAME="foot4570">... operand</A><A
160	href="binary.html#tex2html5"><SUP>5.2</SUP></A></DT>
161	<DD>
162	While <code>abs(x%y) < abs(y)</code> is true mathematically, for
163	floats it may not be true numerically due to roundoff. For
164	example, and assuming a platform on which a Python float is an
165	IEEE 754 double-precision number, in order that <code>-1e-100 % 1e100</code>
166	have the same sign as <code>1e100</code>, the computed result is
167	<code>-1e-100 + 1e100</code>, which is numerically exactly equal
168	to <code>1e100</code>. Function <tt class="function">fmod()</tt> in the <tt class="module">math</tt>
169	module returns a result whose sign matches the sign of the
170	first argument instead, and so returns <code>-1e-100</code> in this case.
171	Which approach is more appropriate depends on the application.
172
173
174	</DD>
175	<DT><A NAME="foot4636">... 1</A><A
176	href="binary.html#tex2html6"><SUP>5.3</SUP></A></DT>
177	<DD>
178	If x is very close to an exact integer multiple of y, it's
179	possible for <code>floor(x/y)</code> to be one larger than
180	<code>(x-x%y)/y</code> due to rounding. In such cases, Python returns
181	the latter result, in order to preserve that <code>divmod(x,y)[0]
182	* y + x % y</code> be very close to <code>x</code>.
183
184
185	</DD>
186	</DL>
187	<DIV CLASS="navigation">
188	<div class='online-navigation'>
189	<p></p><hr />
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221	<span class="release-info">Release 2.4.2, documentation updated on 28 September 2005.</span>
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