user233: In which file can I find the calculation that is called with random()? If it is not too much could you also post the content in your answer? I am using an Arduino Uno and its standard IDE. 
I found this in the "WMath.cpp" but that is not the final calculation. 
void randomSeed(unsigned int seed)
{
  if (seed != 0) {
    srandom(seed);
  }
}

long random(long howbig)
{
  if (howbig == 0) {
    return 0;
  }
  return random() % howbig;
}

long random(long howsmall, long howbig)
{
  if (howsmall >= howbig) {
    return howsmall;
  }
  long diff = howbig - howsmall;
  return random(diff) + howsmall;
}


user7727: Read Peter Bloomfield's answer here: https://arduino.stackexchange.com/a/1482/7727
Then read the following:
For everyone's reference, Arduino's WMath.cpp is found here.
Documentation for AVR-Libc's random() function is here.
Source code for AVR-Libc is found here, as linked-to from here.
I downloaded "avr-libc-2.0.0.tar.bz2.sig    08-Feb-2016" and extracted it. Like Peter said, the source code for "random" is in "avr-libc-2.0.0\libc\stdlib\random.c"
To save you the hassle, here's the source code, with their included copyright and license statement right at the top of it.
/*-
 * Copyright (c) 1990, 1993
 *  The Regents of the University of California.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the University nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 * Posix rand_r function added May 1999 by Wes Peters <wes@softweyr.com>.
 *
 * $Id: random.c 1944 2009-04-01 23:12:20Z arcanum $
 */

/*
 * From:
static char sccsid[] = "@(#)rand.c  8.1 (Berkeley) 6/14/93";
*/

#include <stdlib.h>
#include "sectionname.h"

ATTRIBUTE_CLIB_SECTION
static long
do_random(unsigned long *ctx)
{
    /*
     * Compute x = (7^5 * x) mod (2^31 - 1)
     * wihout overflowing 31 bits:
     *      (2^31 - 1) = 127773 * (7^5) + 2836
     * From "Random number generators: good ones are hard to find",
     * Park and Miller, Communications of the ACM, vol. 31, no. 10,
     * October 1988, p. 1195.
     */
    long hi, lo, x;

    x = *ctx;
    /* Can't be initialized with 0, so use another value. */
    if (x == 0)
        x = 123459876L;
    hi = x / 127773L;
    lo = x % 127773L;
    x = 16807L * lo - 2836L * hi;
    if (x < 0)
        x += 0x7fffffffL;
    return ((*ctx = x) % ((unsigned long)RANDOM_MAX + 1));
}


ATTRIBUTE_CLIB_SECTION
long
random_r(unsigned long *ctx)
{
    return do_random(ctx);
}


static unsigned long next = 1;

ATTRIBUTE_CLIB_SECTION
long
random(void)
{
    return do_random(&next);
}

ATTRIBUTE_CLIB_SECTION
void
srandom(unsigned long seed)
{
    next = seed;
}


user42: The underlying random() function isn't part of the Arduino code. It's actually part of avr-libc. The Arduino IDE only comes with pre-compiled object code for it (as far as I know).
It's open source though. You can get information about it here:

http://www.nongnu.org/avr-libc

If you look down the page a short way, you'll find the "Source code and documentation" link.
The random() function is under libc/stdlib/random.c. I would paste the source code here, but technically I'd have to include a whole copyright notice with it.

233: <p>In which file can I find the calculation that is called with <code>random()</code>? If it is not too much could you also post the content in your answer? I am using an Arduino Uno and its standard IDE. </p>

<p>I found this in the "WMath.cpp" but that is not the final calculation. </p>

<pre class="lang-cpp prettyprint-override"><code>void randomSeed(unsigned int seed)
{
  if (seed != 0) {
    srandom(seed);
  }
}

long random(long howbig)
{
  if (howbig == 0) {
    return 0;
  }
  return random() % howbig;
}

long random(long howsmall, long howbig)
{
  if (howsmall &gt;= howbig) {
    return howsmall;
  }
  long diff = howbig - howsmall;
  return random(diff) + howsmall;
}
</code></pre>
 7727: <p>Read Peter Bloomfield's answer here: <a href="https://arduino.stackexchange.com/a/1482/7727">https://arduino.stackexchange.com/a/1482/7727</a></p>

<p>Then read the following:</p>

<p>For everyone's reference, <a href="https://github.com/arduino/Arduino/blob/master/hardware/arduino/avr/cores/arduino/WMath.cpp" rel="nofollow noreferrer">Arduino's WMath.cpp is found here.</a></p>

<p><a href="http://www.nongnu.org/avr-libc/user-manual/group__avr__stdlib.html#ga114aeb1751119382aaf3340355b22cfd" rel="nofollow noreferrer">Documentation for AVR-Libc's random() function is here.</a></p>

<p><a href="http://download.savannah.gnu.org/releases/avr-libc/" rel="nofollow noreferrer">Source code for AVR-Libc is found here</a>, as linked-to from <a href="http://www.nongnu.org/avr-libc/" rel="nofollow noreferrer">here</a>.</p>

<p>I downloaded "avr-libc-2.0.0.tar.bz2.sig    08-Feb-2016" and extracted it. Like Peter said, the source code for "random" is in "<strong>avr-libc-2.0.0\libc\stdlib\random.c</strong>"</p>

<p>To save you the hassle, here's the source code, with their included copyright and license statement right at the top of it.</p>

<pre><code>/*-
 * Copyright (c) 1990, 1993
 *  The Regents of the University of California.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the University nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 * Posix rand_r function added May 1999 by Wes Peters &lt;wes@softweyr.com&gt;.
 *
 * $Id: random.c 1944 2009-04-01 23:12:20Z arcanum $
 */

/*
 * From:
static char sccsid[] = "@(#)rand.c  8.1 (Berkeley) 6/14/93";
*/

#include &lt;stdlib.h&gt;
#include "sectionname.h"

ATTRIBUTE_CLIB_SECTION
static long
do_random(unsigned long *ctx)
{
    /*
     * Compute x = (7^5 * x) mod (2^31 - 1)
     * wihout overflowing 31 bits:
     *      (2^31 - 1) = 127773 * (7^5) + 2836
     * From "Random number generators: good ones are hard to find",
     * Park and Miller, Communications of the ACM, vol. 31, no. 10,
     * October 1988, p. 1195.
     */
    long hi, lo, x;

    x = *ctx;
    /* Can't be initialized with 0, so use another value. */
    if (x == 0)
        x = 123459876L;
    hi = x / 127773L;
    lo = x % 127773L;
    x = 16807L * lo - 2836L * hi;
    if (x &lt; 0)
        x += 0x7fffffffL;
    return ((*ctx = x) % ((unsigned long)RANDOM_MAX + 1));
}


ATTRIBUTE_CLIB_SECTION
long
random_r(unsigned long *ctx)
{
    return do_random(ctx);
}


static unsigned long next = 1;

ATTRIBUTE_CLIB_SECTION
long
random(void)
{
    return do_random(&amp;next);
}

ATTRIBUTE_CLIB_SECTION
void
srandom(unsigned long seed)
{
    next = seed;
}
</code></pre>
 42: <p>The underlying <code>random()</code> function isn't part of the Arduino code. It's actually part of <code>avr-libc</code>. The Arduino IDE only comes with pre-compiled object code for it (as far as I know).</p>

<p>It's open source though. You can get information about it here:</p>

<ul>
<li><a href="http://www.nongnu.org/avr-libc">http://www.nongnu.org/avr-libc</a></li>
</ul>

<p>If you look down the page a short way, you'll find the "Source code and documentation" link.</p>

<p>The <code>random()</code> function is under <code>libc/stdlib/random.c</code>. I would paste the source code here, but technically I'd have to include a whole copyright notice with it.</p>
