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<a name="fprand">
<h1>
comp.lang.c FAQ list
<font color=blue>&middot;</font>
<a href="../../lib/fprand.html"><!-- qtag -->Question 13.19b</a>
</h1>
<p>
<font face=Helvetica size=8 color=blue><b>Q:</b></font>
How can I generate floating-point random numbers?
</p><p><hr>
<p>
<font face=Helvetica size=8 color=blue><b>A:</b></font>
See question <a href="faqcat1067.html?sec=lib#rand48">13.21</a> for some examples.
<hr><hr><hr>
<a name="gaussian">
<h1>
comp.lang.c FAQ list
<font color=blue>&middot;</font>
<a href="../../lib/gaussian.html"><!-- qtag -->Question 13.20</a>
</h1>
<p>
<font face=Helvetica size=8 color=blue><b>Q:</b></font>
How can I generate random numbers with a
normal or
Gaussian distribution?
</p><p><hr>
<p>
<font face=Helvetica size=8 color=blue><b>A:</b></font>
There are a number of ways of doing this.
</p><OL><li>Exploit
the
Central Limit Theorem
(``law of large numbers'')
and add up several uniformly-distributed random numbers:
<pre>
#include &lt;stdlib.h&gt;
#include &lt;math.h&gt;

#define NSUM 25

double gaussrand()
{
	double x = 0;
	int i;
	for(i = 0; i &lt; NSUM; i++)
		x += (double)rand() / RAND_MAX;

	x -= NSUM / 2.0;
	x /= sqrt(NSUM / 12.0);

	return x;
}
</pre>
(Don't overlook the <TT>sqrt(NSUM&nbsp;/&nbsp;12.)</TT> correction,
though
it's easy to do so accidentally,
especially when <TT>NSUM</TT> is 12.)
<li>Use a method described by
Abramowitz
and
Stegun:
<pre>
#include &lt;stdlib.h&gt;
#include &lt;math.h&gt;

#define PI 3.141592654

double gaussrand()
{
	static double U, V;
	static int phase = 0;
	double Z;

	if(phase == 0) {
		U = (rand() + 1.) / (RAND_MAX + 2.);
		V = rand() / (RAND_MAX + 1.);
		Z = sqrt(-2 * log(U)) * sin(2 * PI * V);
	} else
		Z = sqrt(-2 * log(U)) * cos(2 * PI * V);

	phase = 1 - phase;

	return Z;
}
</pre>
<li>Use a
method
discussed
in
Knuth
and due originally
to Marsaglia:
<pre>
#include &lt;stdlib.h&gt;
#include &lt;math.h&gt;

double gaussrand()
{
	static double V1, V2, S;
	static int phase = 0;
	double X;

	if(phase == 0) {
		do {
			double U1 = (double)rand() / RAND_MAX;
			double U2 = (double)rand() / RAND_MAX;

			V1 = 2 * U1 - 1;
			V2 = 2 * U2 - 1;
			S = V1 * V1 + V2 * V2;
			} while(S &gt;= 1 || S == 0);

		X = V1 * sqrt(-2 * log(S) / S);
	} else
		X = V2 * sqrt(-2 * log(S) / S);

	phase = 1 - phase;

	return X;
}
</pre>
</OL>These
methods
all
generate numbers with mean 0
and standard deviation

1.
(To adjust to some
other distribution,
multiply by
the standard deviation
and add the mean.)
Method 1 is poor ``in the tails''
(especially if <TT>NSUM</TT> is small),
but methods 2 and 3 perform
quite
well.
See the references for more information.
<p><a href="../../lib/sd16.html" rel=subdocument>Additional links</a>
</p>





<p>References:

Knuth Sec. 3.4.1 p. 117
<br>
Box and Muller, ``A Note on the Generation of Random Normal Deviates''
<br>
Marsaglia and Bray, ``A Convenient Method for Generating Normal Variables''
<br>
Abramowitz and Stegun, <I>Handbook of Mathematical Functions</I>
<br>
Press et al., <I>Numerical Recipes in C</I> Sec. 7.2 pp. 288-290
<hr><hr><hr>
<a name="rand48">
<h1>
comp.lang.c FAQ list
<font color=blue>&middot;</font>
<a href="../../lib/rand48.html"><!-- qtag -->Question 13.21</a>
</h1>
<p>
<font face=Helvetica size=8 color=blue><b>Q:</b></font>
I'm porting this program, and it calls a routine
<TT>drand48</TT>,
which my library doesn't have.
What is
it?
</p><p><hr>
<p>
<font face=Helvetica size=8 color=blue><b>A:</b></font>
<TT>drand48</TT>
is a
Unix System V
routine
which
returns floating point random numbers
(presumably

with 48 bits of precision)
in the half-open interval
[0,&nbsp;1)<a href="../../lib/fn76.html" rel=subdocument>[footnote]</a>
.
(Its companion seed routine is <TT>srand48</TT>;
neither is in the C Standard.)
It's easy to write a low-precision replacement:

<pre>
#include &lt;stdlib.h&gt;

double drand48()
{
	return rand() / (RAND_MAX + 1.);
}
</pre>
</p><p>To more accurately simulate <TT>drand48</TT>'s semantics,
you can try to give it closer to
48 bits
worth of precision:
<pre>
#define PRECISION 2.82e14	/* 2**48, rounded up */

double drand48()
{
	double x = 0;
	double denom = RAND_MAX + 1.;
	double need;

	for(need = PRECISION; need &gt; 1;
			need /= (RAND_MAX + 1.)) {
		x += rand() / denom;
		denom *= RAND_MAX + 1.;
	}

	return x;
}
</pre>
</p><p>Before using code like this, though,
beware that it is numerically suspect,
particularly if
(as is usually the case)
the period of <TT>rand</TT> is
on the order of
RAND_MAX.
(If you have a longer-period random number generator available,
such as BSD <TT>random</TT>,
definitely
use it
when simulating <TT>drand48</TT>.)
</p>
<p>References:

PCS Sec. 11 p. 149
<hr><hr><hr>
<a name="exitvsreturn">
<h1>
comp.lang.c FAQ list
<font color=blue>&middot;</font>
<a href="../../lib/exitvsreturn.html"><!-- qtag -->Question 13.22</a>
</h1>
<p>
<font face=Helvetica size=8 color=blue><b>Q:</b></font>
Is <TT>exit(status)</TT> truly equivalent
to returning the same <TT>status</TT> from <TT>main</TT>?
</p>
<p><hr>
<p>
<font face=Helvetica size=8 color=blue><b>A:</b></font>
See question <a href="faqcat7d4b.html?sec=ansi#exitvsreturn">11.16</a>.
<hr><hr><hr>
<a name="memmove">
<h1>
comp.lang.c FAQ list
<font color=blue>&middot;</font>
<a href="../../lib/memmove.html"><!-- qtag -->Question 13.23</a>
</h1>
<p>
<font face=Helvetica size=8 color=blue><b>Q:</b></font>
What's the difference between
<TT>memcpy</TT> and
<TT>memmove</TT>?

</p>
<p><hr>
<p>
<font face=Helvetica size=8 color=blue><b>A:</b></font>
See question <a href="faqcat7d4b.html?sec=ansi#memmove">11.25</a>.
<hr><hr><hr>
<a name="oldlibfcns">
<h1>
comp.lang.c FAQ list
<font color=blue>&middot;</font>
<a href="../../lib/oldlibfcns.html"><!-- qtag -->Question 13.24</a>
</h1>
<p>
<font face=Helvetica size=8 color=blue><b>Q:</b></font>
I'm trying to port this old program.
Why do I get ``undefined external'' errors
for some library functions?
</p><p><hr>
<p>
<font face=Helvetica size=8 color=blue><b>A:</b></font>
Some
old or
semistandard functions have been renamed or replaced over the years;
<br>if you need:/you should instead:
<dl><dt><TT>index</TT>
</dt><dd>use <TT>strchr</TT>.
</dd><dt><TT>rindex</TT>
</dt><dd>use <TT>strrchr</TT>.
</dd><dt><TT>bcopy</TT>
</dt><dd>use
<TT>memmove</TT>,
after interchanging the first and second arguments
(see also question
<a href="faqcat7d4b.html?sec=ansi#memmove">11.25</a>).
</dd><dt><TT>bcmp</TT>
</dt><dd>use <TT>memcmp</TT>.
</dd><dt><TT>bzero</TT>
</dt><dd>use <TT>memset</TT>,
with a second argument of 0.
</dd></dl></p><p>See also questions <a href="faqcat1d60.html?sec=stdio#sprintfret">12.22</a>
and <a href="faqcat1067.html?sec=lib#rand48">13.21</a>.
</p>
<p>References:

PCS Sec. 11
<hr><hr><hr>
<a name="extlibs">
<h1>
comp.lang.c FAQ list
<font color=blue>&middot;</font>
<a href="../../lib/extlibs.html"><!-- qtag -->Question 13.25</a>
</h1>
<p>
<font face=Helvetica size=8 color=blue><b>Q:</b></font>
I
keep getting
errors due to library functions being undefined,
but I'm #including all
the right header files.
</p><p><hr>
<p>
<font face=Helvetica size=8 color=blue><b>A:</b></font>




In the general case of calling code in an
external library,
using <TT>#include</TT> to pull in
the right header file(s) is only half
of the story; you also have to tell the linker to search the
external library itself.
The declarations in the header file
only tell the compiler how to call the external functions;
the header file doesn't supply the definitions of the external
functions, or tell the compiler/linker where to find those
definitions.
</p><p>In some cases
(especially if the functions are nonstandard)
obtaining
those definitions
may require explicitly asking
for the correct libraries to be
searched
when you link the program.
(Some systems may be able to arrange
that whenever you <TT>#include</TT> a header,
its associated library, if nonstandard,
is automatically requested at link time,
but such a facility is not
widespread.)
See also questions
<a href="faqcat204f.html?sec=cpp#missinghdr">10.11</a>,
<a href="faqcat7d4b.html?sec=ansi#preansilib">11.30</a>,
<a href="faqcat1067.html?sec=lib#libsearch">13.26</a>,
<a href="faqcat973e.html?sec=fp#libm">14.3</a>,
and
<a href="faqcatea63.html?sec=osdep#networking">19.40</a>.
<hr><hr><hr>
<a name="libsearch">
<h1>
comp.lang.c FAQ list
<font color=blue>&middot;</font>
<a href="../../lib/libsearch.html"><!-- qtag -->Question 13.26</a>
</h1>
<p>
<font face=Helvetica size=8 color=blue><b>Q:</b></font>
I'm still getting errors due to library functions being undefined,
even though I'm
explicitly
requesting the right libraries
while linking.
</p><p><hr>
<p>
<font face=Helvetica size=8 color=blue><b>A:</b></font>
Many
linkers make one pass
over the list of object files and libraries you specify,
and extract from libraries
only those modules
which satisfy references
which have so far come up as undefined.
Therefore, the
order in which libraries are
listed
with respect to object files
(and each other)
is significant;
usually,
you
want to
search the libraries last.
</p><p>For example,
under
Unix,
a command line like
<pre>
	cc -lm myprog.c		# WRONG
</pre>
usually won't work.
Instead,
put any <TT>-l</TT> options
at
the end of the command line:
<pre>
	cc myprog.c -lm
</pre>

</p><p>If you list a library first,
the linker doesn't know that it

needs anything out of it yet,
and
passes it by.
See also question <a href="faqcat1067.html?sec=lib#endundef">13.28</a>.
<hr><hr><hr>
<a name="bloat">
<h1>
comp.lang.c FAQ list
<font color=blue>&middot;</font>
<a href="../../lib/bloat.html"><!-- qtag -->Question 13.27</a>
</h1>
<p>
<font face=Helvetica size=8 color=blue><b>Q:</b></font>
Why is my simple program,
which hardly does more than print ``Hello, world!''
in a window,
compiling to such a huge executable
(several hundred K)?
Should I <TT>#include</TT> fewer header files?
</p><p><hr>
<p>
<font face=Helvetica size=8 color=blue><b>A:</b></font>
What you're seeing is the current
(poor)
state of the ``art'' in library design.
As run-time libraries accrete more and more features
(especially
having to do
with
Graphical User Interfaces),
and when one library function calls another library function to 
do part of its job
(which ought to be a Good Thing;
that's what library functions are for),
it
can happen
that
calling anything in the library
(particularly something relatively powerful like <TT>printf</TT>)
eventually pulls in practically everything
else,
leading to horribly bloated executables.
</p><p>#including fewer header files probably won't help,
because declaring a few functions which you don't call
(which is mostly all that happens when you #include a header 
you don't need)
shouldn't result in those functions being placed in your 
executable,
unless
they actually do get called.
See also question <a href="faqcat1067.html?sec=lib#extlibs">13.25</a>.
</p><p>You may be able to track down
and derail
a
chain

of unnecessarily-coupled functions which are 

bloating your executable,
or maybe complain to your vendor to clean up the libraries.
</p>
<p>References:

H&amp;S Sec. 4.8.6 pp. 103-4
<hr><hr><hr>
<a name="endundef">
<h1>
comp.lang.c FAQ list
<font color=blue>&middot;</font>
<a href="../../lib/endundef.html"><!-- qtag -->Question 13.28</a>
</h1>
<p>
<font face=Helvetica size=8 color=blue><b>Q:</b></font>
What does it mean when the linker says that <TT>_end</TT> is undefined?
</p><p><hr>
<p>
<font face=Helvetica size=8 color=blue><b>A:</b></font>
That message
is a quirk of the old Unix linkers.
You
get
an error about <TT>_end</TT> being undefined
only
when other
symbols
are undefined,
too--fix
the others,
and the error about <TT>_end</TT> will disappear.
(See also questions <a href="faqcat1067.html?sec=lib#extlibs">13.25</a>
and <a href="faqcat1067.html?sec=lib#libsearch">13.26</a>.)
<hr><hr><hr>
<a name="noprintf">
<h1>
comp.lang.c FAQ list
<font color=blue>&middot;</font>
<a href="../../lib/noprintf.html"><!-- qtag -->Question 13.29</a>
</h1>
<p>
<font face=Helvetica size=8 color=blue><b>Q:</b></font>
My compiler is complaining that <TT>printf</TT> is undefined!
How can this be?
It's the world's most popular C function...
</p><p><hr>
<p>
<font face=Helvetica size=8 color=blue><b>A:</b></font>

Allegedly, there are C compilers for Microsoft Windows
which do not support <TT>printf</TT>,
on the argument that
<TT>printf</TT> is for printing to old-fashioned terminals,
while under Windows the right way to display text
is to call xxx to open a window
and then xxx to display text in it.
It may be possible to convince such a compiler
that what you are writing is a
``console application''
meaning that it will
take care of opening
a ``console window''
for you automatically,
and condescend to let you call <TT>printf</TT> to print stuff to it.
</p><p>See also question <a href="faqcatea63.html?sec=osdep#waitforkey">19.4b</a>.
<hr><hr><hr>
<hr>
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