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
|
<HTML>
<!--
-- Copyright (c) 1996-1999
-- Silicon Graphics Computer Systems, Inc.
--
-- Permission to use, copy, modify, distribute and sell this software
-- and its documentation for any purpose is hereby granted without fee,
-- provided that the above copyright notice appears in all copies and
-- that both that copyright notice and this permission notice appear
-- in supporting documentation. Silicon Graphics makes no
-- representations about the suitability of this software for any
-- purpose. It is provided "as is" without express or implied warranty.
--
-- Copyright (c) 1994
-- Hewlett-Packard Company
--
-- Permission to use, copy, modify, distribute and sell this software
-- and its documentation for any purpose is hereby granted without fee,
-- provided that the above copyright notice appears in all copies and
-- that both that copyright notice and this permission notice appear
-- in supporting documentation. Hewlett-Packard Company makes no
-- representations about the suitability of this software for any
-- purpose. It is provided "as is" without express or implied warranty.
--
-->
<Head>
<Title>Random Number Generator</Title>
<!-- Generated by htmldoc -->
</HEAD>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="CorpID.gif"
ALT="SGI" HEIGHT="43" WIDTH="151">
<!--end header-->
<BR Clear>
<H1>Random Number Generator</H1>
<Table CellPadding=0 CellSpacing=0 width=100%>
<TR>
<TD Align=left><Img src = "functors.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD>
<TD Align=right><Img src = "concept.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD>
</TR>
<TR>
<TD Align=left VAlign=top><b>Category</b>: functors</TD>
<TD Align=right VAlign=top><b>Component type</b>: concept</TD>
</TR>
</Table>
<h3>Description</h3>
A Random Number Generator is a <A href="functors.html">function object</A> that can be used to
generate a random sequence of integers. That is: if <tt>f</tt> is a Random
Number Generator and <tt>N</tt> is a positive integer, then <tt>f(N)</tt> will return
an integer less than <tt>N</tt> and greater than or equal to <tt>0</tt>. If <tt>f</tt> is
called many times with the same value of <tt>N</tt>, it will yield a sequence
of numbers that is uniformly distributed <A href="#1">[1]</A> in the range <tt>[0, N)</tt>. <A href="#2">[2]</A>
<h3>Refinement of</h3>
<A href="UnaryFunction.html">Unary Function</A>
<h3>Associated types</h3>
<Table border>
<TR>
<TD VAlign=top>
Argument type
</TD>
<TD VAlign=top>
The type of the Random Number Generator's argument. This must
be an integral type.
</TD>
</TR>
<TR>
<TD VAlign=top>
Result type
</TD>
<TD VAlign=top>
The type returned when the Random Number Generator is called. It must
be the same as the argument type.
</TD>
</tr>
</table>
<h3>Notation</h3>
<Table>
<TR>
<TD VAlign=top>
<tt>F</tt>
</TD>
<TD VAlign=top>
A type that is a model of Random Number Generator.
</TD>
</TR>
<TR>
<TD VAlign=top>
<tt>Integer</tt>
</TD>
<TD VAlign=top>
The argument type of <tt>F</tt>.
</TD>
</TR>
<TR>
<TD VAlign=top>
<tt>f</tt>
</TD>
<TD VAlign=top>
Object of type <tt>F</tt>.
</TD>
</TR>
<TR>
<TD VAlign=top>
<tt>N</tt>
</TD>
<TD VAlign=top>
Object of type <tt>Integer</tt>
</TD>
</tr>
</table>
<h3>Definitions</h3>
The <i>domain</i> of a Random Number Generator (<i>i.e.</i> the set
of permissible values for its argument) is the set of numbers that are
greater than zero and less than some maximum value.
<P>
The <i>range</i> of a Random Number Generator is the set of nonnegative
integers that are less than the Random Number Generator's argument.
<h3>Valid expressions</h3>
None, except for those defined by <A href="UnaryFunction.html">Unary Function</A>.
<h3>Expression semantics</h3>
<Table border>
<TR>
<TH>
Name
</TH>
<TH>
Expression
</TH>
<TH>
Precondition
</TH>
<TH>
Semantics
</TH>
<TH>
Postcondition
</TH>
</TR>
<TR>
<TD VAlign=top>
Function call
</TD>
<TD VAlign=top>
<tt>f(N)</tt>
</TD>
<TD VAlign=top>
<tt>N</tt> is positive.
</TD>
<TD VAlign=top>
Returns a pseudo-random number of type <tt>Integer</tt>. <A href="#2">[2]</A>
</TD>
<TD VAlign=top>
The return value is less than <tt>N</tt>, and greater than or equal to 0.
</TD>
</tr>
</table>
<h3>Complexity guarantees</h3>
<h3>Invariants</h3>
<Table border>
<TR>
<TD VAlign=top>
Uniformity
</TD>
<TD VAlign=top>
In the limit as <tt>f</tt> is called many times with the same argument
<tt>N</tt>, every integer in the range <tt>[0, N)</tt> will appear an equal number
of times.
</TD>
</tr>
</table>
<h3>Models</h3>
<h3>Notes</h3>
<P><A name="1">[1]</A>
Uniform distribution means that all of the numbers in the range
<tt>[0, N)</tt> appear with equal frequency. Or, to put it differently,
the probability for obtaining any particular value is <tt>1/N</tt>.
<P><A name="2">[2]</A>
Random number generators are a very subtle subject: a good random
number generator must satisfy many statistical properties beyond
uniform distribution. See section 3.4 of Knuth for a discussion of
what it means for a sequence to be random, and section 3.2 for several
algorithms that may be used to write random number generators.
(D. E. Knuth, <i>The Art of Computer
Programming. Volume 2: Seminumerical Algorithms</i>, third edition.
Addison-Wesley, 1998.)
<h3>See also</h3>
<!--start footer-->
<HR SIZE="6">
<A href="http://www.sgi.com/"><IMG SRC="surf.gif" HEIGHT="54" WIDTH="54"
ALT="[Silicon Surf]"></A>
<A HREF="index.html"><IMG SRC="stl_home.gif"
HEIGHT="54" WIDTH="54" ALT="[STL Home]"></A>
<BR>
<FONT SIZE="-2">
<A href="http://www.sgi.com/Misc/sgi_info.html" TARGET="_top">Copyright ©
1999 Silicon Graphics, Inc.</A> All Rights Reserved.</FONT>
<FONT SIZE="-3"><a href="http://www.sgi.com/Misc/external.list.html" TARGET="_top">TrademarkInformation</A>
</FONT>
<P>
</BODY>
</HTML>
|
