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