1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
|
<html lang="en">
<head>
<title>Bit Manipulations - Untitled</title>
<meta http-equiv="Content-Type" content="text/html">
<meta name="description" content="Untitled">
<meta name="generator" content="makeinfo 4.11">
<link title="Top" rel="start" href="index.html#Top">
<link rel="up" href="Numeric-Data-Types.html#Numeric-Data-Types" title="Numeric Data Types">
<link rel="prev" href="Integer-Data-Types.html#Integer-Data-Types" title="Integer Data Types">
<link rel="next" href="Logical-Values.html#Logical-Values" title="Logical Values">
<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
<meta http-equiv="Content-Style-Type" content="text/css">
<style type="text/css"><!--
pre.display { font-family:inherit }
pre.format { font-family:inherit }
pre.smalldisplay { font-family:inherit; font-size:smaller }
pre.smallformat { font-family:inherit; font-size:smaller }
pre.smallexample { font-size:smaller }
pre.smalllisp { font-size:smaller }
span.sc { font-variant:small-caps }
span.roman { font-family:serif; font-weight:normal; }
span.sansserif { font-family:sans-serif; font-weight:normal; }
--></style>
</head>
<body>
<div class="node">
<p>
<a name="Bit-Manipulations"></a>
Next: <a rel="next" accesskey="n" href="Logical-Values.html#Logical-Values">Logical Values</a>,
Previous: <a rel="previous" accesskey="p" href="Integer-Data-Types.html#Integer-Data-Types">Integer Data Types</a>,
Up: <a rel="up" accesskey="u" href="Numeric-Data-Types.html#Numeric-Data-Types">Numeric Data Types</a>
<hr>
</div>
<h3 class="section">4.5 Bit Manipulations</h3>
<p>Octave provides a number of functions for the manipulation of numeric
values on a bit by bit basis. The basic functions to set and obtain the
values of individual bits are <code>bitset</code> and <code>bitget</code>.
<!-- ./general/bitset.m -->
<p><a name="doc_002dbitset"></a>
<div class="defun">
— Function File: <var>x</var> = <b>bitset</b> (<var>a, n</var>)<var><a name="index-bitset-250"></a></var><br>
— Function File: <var>x</var> = <b>bitset</b> (<var>a, n, v</var>)<var><a name="index-bitset-251"></a></var><br>
<blockquote><p>Set or reset bit(s) <var>n</var> of unsigned integers in <var>a</var>.
<var>v</var> = 0 resets and <var>v</var> = 1 sets the bits.
The lowest significant bit is: <var>n</var> = 1
<pre class="example"> dec2bin (bitset (10, 1))
1011
</pre>
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dbitand.html#doc_002dbitand">bitand</a>, <a href="doc_002dbitor.html#doc_002dbitor">bitor</a>, <a href="doc_002dbitxor.html#doc_002dbitxor">bitxor</a>, <a href="doc_002dbitget.html#doc_002dbitget">bitget</a>, <a href="doc_002dbitcmp.html#doc_002dbitcmp">bitcmp</a>, <a href="doc_002dbitshift.html#doc_002dbitshift">bitshift</a>, <a href="doc_002dbitmax.html#doc_002dbitmax">bitmax</a>.
</p></blockquote></div>
<!-- ./general/bitget.m -->
<p><a name="doc_002dbitget"></a>
<div class="defun">
— Function File: <var>X</var> = <b>bitget</b> (<var>a,n</var>)<var><a name="index-bitget-252"></a></var><br>
<blockquote><p>Return the status of bit(s) <var>n</var> of unsigned integers in <var>a</var>
the lowest significant bit is <var>n</var> = 1.
<pre class="example"> bitget (100, 8:-1:1)
0 1 1 0 0 1 0 0
</pre>
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dbitand.html#doc_002dbitand">bitand</a>, <a href="doc_002dbitor.html#doc_002dbitor">bitor</a>, <a href="doc_002dbitxor.html#doc_002dbitxor">bitxor</a>, <a href="doc_002dbitset.html#doc_002dbitset">bitset</a>, <a href="doc_002dbitcmp.html#doc_002dbitcmp">bitcmp</a>, <a href="doc_002dbitshift.html#doc_002dbitshift">bitshift</a>, <a href="doc_002dbitmax.html#doc_002dbitmax">bitmax</a>.
</p></blockquote></div>
<p>The arguments to all of Octave's bitwise operations can be scalar or
arrays, except for <code>bitcmp</code>, whose <var>k</var> argument must a
scalar. In the case where more than one argument is an array, then all
arguments must have the same shape, and the bitwise operator is applied
to each of the elements of the argument individually. If at least one
argument is a scalar and one an array, then the scalar argument is
duplicated. Therefore
<pre class="example"> bitget (100, 8:-1:1)
</pre>
<p>is the same as
<pre class="example"> bitget (100 * ones (1, 8), 8:-1:1)
</pre>
<p>It should be noted that all values passed to the bit manipulation
functions of Octave are treated as integers. Therefore, even though the
example for <code>bitset</code> above passes the floating point value
<code>10</code>, it is treated as the bits <code>[1, 0, 1, 0]</code> rather than the
bits of the native floating point format representation of <code>10</code>.
<p>As the maximum value that can be represented by a number is important
for bit manipulation, particularly when forming masks, Octave supplies
the function <code>bitmax</code>.
<!-- bitfcns.cc -->
<p><a name="doc_002dbitmax"></a>
<div class="defun">
— Built-in Function: <b>bitmax</b> ()<var><a name="index-bitmax-253"></a></var><br>
<blockquote><p>Return the largest integer that can be represented as a floating point
value. On IEEE-754 compatible systems, <code>bitmax</code> is <code>2^53 - 1</code>.
</p></blockquote></div>
<p>This is the double precision version of the functions <code>intmax</code>,
previously discussed.
<p>Octave also includes the basic bitwise 'and', 'or' and 'exclusive or'
operators.
<!-- bitfcns.cc -->
<p><a name="doc_002dbitand"></a>
<div class="defun">
— Built-in Function: <b>bitand</b> (<var>x, y</var>)<var><a name="index-bitand-254"></a></var><br>
<blockquote><p>Return the bitwise AND of non-negative integers.
<var>x</var>, <var>y</var> must be in the range [0,bitmax]
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dbitor.html#doc_002dbitor">bitor</a>, <a href="doc_002dbitxor.html#doc_002dbitxor">bitxor</a>, <a href="doc_002dbitset.html#doc_002dbitset">bitset</a>, <a href="doc_002dbitget.html#doc_002dbitget">bitget</a>, <a href="doc_002dbitcmp.html#doc_002dbitcmp">bitcmp</a>, <a href="doc_002dbitshift.html#doc_002dbitshift">bitshift</a>, <a href="doc_002dbitmax.html#doc_002dbitmax">bitmax</a>.
</p></blockquote></div>
<!-- bitfcns.cc -->
<p><a name="doc_002dbitor"></a>
<div class="defun">
— Built-in Function: <b>bitor</b> (<var>x, y</var>)<var><a name="index-bitor-255"></a></var><br>
<blockquote><p>Return the bitwise OR of non-negative integers.
<var>x</var>, <var>y</var> must be in the range [0,bitmax]
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dbitor.html#doc_002dbitor">bitor</a>, <a href="doc_002dbitxor.html#doc_002dbitxor">bitxor</a>, <a href="doc_002dbitset.html#doc_002dbitset">bitset</a>, <a href="doc_002dbitget.html#doc_002dbitget">bitget</a>, <a href="doc_002dbitcmp.html#doc_002dbitcmp">bitcmp</a>, <a href="doc_002dbitshift.html#doc_002dbitshift">bitshift</a>, <a href="doc_002dbitmax.html#doc_002dbitmax">bitmax</a>.
</p></blockquote></div>
<!-- bitfcns.cc -->
<p><a name="doc_002dbitxor"></a>
<div class="defun">
— Built-in Function: <b>bitxor</b> (<var>x, y</var>)<var><a name="index-bitxor-256"></a></var><br>
<blockquote><p>Return the bitwise XOR of non-negative integers.
<var>x</var>, <var>y</var> must be in the range [0,bitmax]
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dbitand.html#doc_002dbitand">bitand</a>, <a href="doc_002dbitor.html#doc_002dbitor">bitor</a>, <a href="doc_002dbitset.html#doc_002dbitset">bitset</a>, <a href="doc_002dbitget.html#doc_002dbitget">bitget</a>, <a href="doc_002dbitcmp.html#doc_002dbitcmp">bitcmp</a>, <a href="doc_002dbitshift.html#doc_002dbitshift">bitshift</a>, <a href="doc_002dbitmax.html#doc_002dbitmax">bitmax</a>.
</p></blockquote></div>
<p>The bitwise 'not' operator is a unary operator that performs a logical
negation of each of the bits of the value. For this to make sense, the
mask against which the value is negated must be defined. Octave's
bitwise 'not' operator is <code>bitcmp</code>.
<!-- ./general/bitcmp.m -->
<p><a name="doc_002dbitcmp"></a>
<div class="defun">
— Function File: <b>bitcmp</b> (<var>a, k</var>)<var><a name="index-bitcmp-257"></a></var><br>
<blockquote><p>Return the <var>k</var>-bit complement of integers in <var>a</var>. If
<var>k</var> is omitted <code>k = log2 (bitmax) + 1</code> is assumed.
<pre class="example"> bitcmp(7,4)
8
dec2bin(11)
1011
dec2bin(bitcmp(11, 6))
110100
</pre>
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dbitand.html#doc_002dbitand">bitand</a>, <a href="doc_002dbitor.html#doc_002dbitor">bitor</a>, <a href="doc_002dbitxor.html#doc_002dbitxor">bitxor</a>, <a href="doc_002dbitset.html#doc_002dbitset">bitset</a>, <a href="doc_002dbitget.html#doc_002dbitget">bitget</a>, <a href="doc_002dbitcmp.html#doc_002dbitcmp">bitcmp</a>, <a href="doc_002dbitshift.html#doc_002dbitshift">bitshift</a>, <a href="doc_002dbitmax.html#doc_002dbitmax">bitmax</a>.
</p></blockquote></div>
<p>Octave also includes the ability to left-shift and right-shift values bitwise.
<!-- bitfcns.cc -->
<p><a name="doc_002dbitshift"></a>
<div class="defun">
— Built-in Function: <b>bitshift</b> (<var>a, k</var>)<var><a name="index-bitshift-258"></a></var><br>
— Built-in Function: <b>bitshift</b> (<var>a, k, n</var>)<var><a name="index-bitshift-259"></a></var><br>
<blockquote><p>Return a <var>k</var> bit shift of <var>n</var>-digit unsigned
integers in <var>a</var>. A positive <var>k</var> leads to a left shift.
A negative value to a right shift. If <var>n</var> is omitted it defaults
to log2(bitmax)+1.
<var>n</var> must be in the range [1,log2(bitmax)+1] usually [1,33]
<pre class="example"> bitshift (eye (3), 1)
<p>2 0 0
0 2 0
0 0 2
bitshift (10, [-2, -1, 0, 1, 2])
2 5 10 20 40
<!-- FIXME - restore this example when third arg is allowed to be an array. -->
<!-- bitshift ([1, 10], 2, [3,4]) -->
<!-- @result{} 4 8 -->
</pre>
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dbitand.html#doc_002dbitand">bitand</a>, <a href="doc_002dbitor.html#doc_002dbitor">bitor</a>, <a href="doc_002dbitxor.html#doc_002dbitxor">bitxor</a>, <a href="doc_002dbitset.html#doc_002dbitset">bitset</a>, <a href="doc_002dbitget.html#doc_002dbitget">bitget</a>, <a href="doc_002dbitcmp.html#doc_002dbitcmp">bitcmp</a>, <a href="doc_002dbitmax.html#doc_002dbitmax">bitmax</a>.
</p></blockquote></div>
<p>Bits that are shifted out of either end of the value are lost. Octave
also uses arithmetic shifts, where the sign bit of the value is kept
during a right shift. For example
<pre class="example"> bitshift (-10, -1)
-5
bitshift (int8 (-1), -1)
-1
</pre>
<p>Note that <code>bitshift (int8 (-1), -1)</code> is <code>-1</code> since the bit
representation of <code>-1</code> in the <code>int8</code> data type is <code>[1, 1,
1, 1, 1, 1, 1, 1]</code>.
</body></html>
|
