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<book id="enigma-documentation.xml" lang="en">
  <title>Enigma</title>
<!-- %**end of header -->
  <bookinfo>
    <legalnotice>
      <para>This manual is for Enigma, version 0.1.
Copyright &copy; 2010 Niels Serup</para>
      <blockquote>
        <para>Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with no
Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.  A
copy of the license is included in the section entitled "GNU Free
Documentation License".</para>
        <para>This document is also available under the terms of the Creative Commons
Attribution-Share Alike 3.0 (or any later version) Unported license. A
copy of the license is available at
<ulink url="http://creativecommons.org/licenses/by-sa/3.0/legalcode">http://creativecommons.org/licenses/by-sa/3.0/legalcode</ulink>.</para>
      </blockquote>
   
    </legalnotice>
</bookinfo>
  <chapter label="" xreflabel="Enigma" id="Top">
    <title>Enigma</title>
    <para>This manual is for Enigma, version 0.1.
Copyright &copy; 2010 Niels Serup</para>
    <blockquote>
      <para>Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with no
Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.  A
copy of the license is included in the section entitled "GNU Free
Documentation License".</para>
      <para>This document is also available under the terms of the Creative Commons
Attribution-Share Alike 3.0 (or any later version) Unported license. A
copy of the license is available at
<ulink url="http://creativecommons.org/licenses/by-sa/3.0/legalcode">http://creativecommons.org/licenses/by-sa/3.0/legalcode</ulink>.</para>
    </blockquote>
    <para>New versions of this manual will be available at
<ulink url="http://metanohi.org/projects/enigma/">http://metanohi.org/projects/enigma/</ulink>.</para>
  </chapter>

  <chapter label="1" id="Introduction">
    <title>A short introduction</title>
    <para>Today, in the world of programming, the commonly used programming
languages have &mdash; to some extent &mdash; adapted the same basic
syntax. Both C, C++, Java, Python and Ruby (and others) all share
several paradigms, even though they are still very different. Enigma, on
the other hand, is very different from the &ldquo;common&rdquo; languages. See
this small program to get an idea of Enigma:</para>
    <screen>{/a,b/
    a 2 ! multiply = c;
    b c ! add = return;
} = odd-add;

9 4 ! odd-add | stdout temp ! write;
</screen>
    <para role="continues">Here, 9 is first multiplied with 2 and then added to 4. The
program then prints the result (22).</para>
    <para>With only a few constructs and built-in variables, Enigma is quite small
and relatively simple. Any logic can be expressed in Enigma. The above
example may seem odd, but its aspects will be dealt with in the next
chapter.</para>
    <para>Enigma is <emphasis>not</emphasis> the kind of programming language that likes to
control programmers. When programming in Enigma, one creates functions
that call other functions &mdash; instead of creating functions that are
called by built-in functions.</para>
    <para>On the other hand, Enigma is very restrictive. There are limits to
certain things. If these limits were not present, chaos would
ensue. Perhaps.</para>
    <para><indexterm role="cp"><primary>pointers</primary></indexterm>Like many other languages, Enigma is quite fond of pointers. In Enigma,
all variables are pointers. When <literal>x</literal> is assigned to <literal>a</literal>, and
<literal>b</literal> is assigned to <literal>a</literal>, changing <literal>b</literal> also changes
<literal>a</literal>. As a matter of fact, when two pointers points to the same
place, they are <emphasis role="bold">forever</emphasis> linked together.</para>
    <para>Enigma is not recommended for serious use. Use with <emphasis role="bold">caution</emphasis>!</para>
  </chapter>

  <chapter label="2" id="Language">
    <title>The language</title>
    <para>Enigma consists of functions. Any file being parsed is a
function. Within functions there can be local variables. These variables
are to disappear when the function exits.</para>
    <para>Functions have return values. These values can be determined by the
programmer.</para>
    <para>Within functions, there are commands. These commands constitute the very
base of Enigma. Commands can interact with built-in functions, meaning
that writing to and reading from files, calculating, as well as
manipulating strings and lists, is possible.</para>
    <para>There are no simple types. Enigma lies in the world of objects. Numbers,
strings, lists.. It's just objects. Also, all commands must end with a
semicolon<literal>;</literal></para>

    <sect1 label="2.1" id="Operators">
      <title>Operators</title>
      <para><indexterm role="cp"><primary>operators</primary></indexterm>Enigma has 4 operators: <literal>!</literal>, <literal>=</literal>, <literal>|</literal>, and
<literal>*</literal>. <literal>!</literal> and <literal>=</literal> are the most important ones.</para>
      <para>To assign values to variables, use the <literal>=</literal> operator. For example:</para>
      <screen>obj = hello-string;
</screen>
      <para>Here, the variable <literal>hello-string</literal> receives the object <literal>obj</literal>. Note
the syntax. The objects comes first. Unless <literal>hello-string</literal> is
already defined, it is created as a local variable.</para>
      <para>Now, say we have a function called <literal>think</literal> and we want to send
objects to it. This is how that's done:</para>
      <screen>obj1 obj2 obj3 ! think;
</screen>
      <para>There are no limits to the amount of objects that can be sent to a
function. Whitespace characters are used to separate objects, also when
assigning them to a variable. There <emphasis>is</emphasis> a difference between
using one object and more objects as arguments, though. When using only
one object, that object is simply used, but when using more objects, a
list containing all objects is created and transmitted instead. So, in
reality, when assigning two or more objects to a variable, the variable
points to a list with the objects. More about lists later.</para>
      <para>The <literal>|</literal> operator is merely a shortcut operator. It can merge
several commands into one, long command. See the following example:</para>
      <screen># Long version
a ! b = c;
d c ! e = c;
# Short version
a ! b | d temp ! e = c;
</screen>
      <para>Here, <literal>a</literal> is sent to <literal>b</literal>, which is then &mdash; together with
<literal>d</literal> &mdash; sent to <literal>e</literal> and saved in <literal>c</literal>. The <literal>|</literal> acts
like the semicolon, but it copies the return value of the last function
(in this case <literal>b</literal>) and stores the value in the local variable
<literal>temp</literal>. Hackers are encouraged to use this operator.</para>
      <para>The final operator, <literal>*</literal>, has the same function as <literal>=</literal>, except
that it works on a global level. So, if the code is <literal>b = a;</literal> and
<literal>a</literal> does not exist, it is created &mdash; in the global space.</para>
    </sect1>

    <sect1 label="2.2" id="Numbers">
      <title>Numbers</title>
      <para><indexterm role="cp"><primary>numbers</primary></indexterm>Numbers in Enigma can be arbitrarily large. They are written as one
usually writes numbers. Currently only the decimal system is supported.</para>
      <screen>7587 = age;
2556 ! numfunc;
</screen>
    </sect1>

    <sect1 label="2.3" id="Strings">
      <title>Strings</title>
      <para><indexterm role="cp"><primary>strings</primary></indexterm><indexterm role="cp"><primary>characters</primary></indexterm>Strings are defined using the <literal>"</literal> character.</para>
      <screen>"This is a string!" " This too!" ! add;
"A" = A;
"Now comes
a newline" = nl;
"\"\\\n\t\
" = escaped;
</screen>
    </sect1>

    <sect1 label="2.4" id="Lists">
      <title>Lists</title>
      <para><indexterm role="cp"><primary>lists</primary></indexterm><indexterm role="cp"><primary>arrays</primary></indexterm>Lists are special in Enigma. They are used a lot, but unlike eg. numbers
and strings they cannot be defined in their own syntax. When one writes
this:</para>
      <screen>123 "witch" = lst;
</screen>
      <para>..one creates a list. Lists can be nested.</para>
    </sect1>

    <sect1 label="2.5" id="Booleans">
      <title>Booleans</title>
      <para><indexterm role="cp"><primary>booleans</primary></indexterm>Booleans are used a lot in Enigma. The predefined variables <literal>true</literal>
and <literal>false</literal> can be used.</para>
    </sect1>

    <sect1 label="2.6" id="Files">
      <title>Files</title>
      <para><indexterm role="cp"><primary>files</primary></indexterm>Files can only be created using the built-in function <literal>open</literal>. Files
are either readable or writeable. If a file is writeable, text written
to the file may optionally be appended to any existing text.</para>
      <para><indexterm role="cp"><primary>read</primary></indexterm><indexterm role="cp"><primary>write</primary></indexterm><indexterm role="cp"><primary>open</primary></indexterm><indexterm role="cp"><primary>close</primary></indexterm></para>
      <screen>"a" "r" ! open = f1;
"b" "w" ! open = f2;
"c" "a" ! open = f3;

# Read one character
f1 ! read | stdout temp ! write;
# Write a string
f2 "Aaar" ! write;
# Append a string
f3 "Ouu" ! write;

f1!close;f2!close;f3!close;
</screen>
      <para>To read an entire file, one must use a loop
construct. See <xref linkend="Loops"></xref>. When there are no more characters left, the
<literal>read</literal> function returns an empty string. Using equality testing,
reading a complete file is thus possible. See <xref linkend="Conditionals"></xref>.</para>
      <screen>filename "r" ! open = f;
{f ! read = c; stdout c ! write; c "" ! equal ! not = return;} ! loop;
</screen>
      <para>At this point, it may not be obvious why this works. This will be
explained in the next sections.</para>
    </sect1>

    <sect1 label="2.7" id="Functions">
      <title>Functions</title>
      <para><indexterm role="cp"><primary>functions</primary></indexterm>Functions are defined and called using the following syntax:</para>
      <screen># Defining them
{stdout "Hello" ! write;} = func;
{/x,y/stdout "x=" x ", y=" y!write;} = coorprint;
{stdout args ! write;} = aprint;

# Calling them
!func;                 # Outputs "Hello"
52 12 ! coorprint;     # Outputs "x=52, y=12"
999 "abc" 21 ! aprint; # Outputs "999 abc 21"
</screen>
      <para>Arguments can thus be accessed either by using the <literal>/.../</literal> syntax
in the beginning of the function or by using the local <literal>args</literal>
variable. Furthermore, to make <emphasis>all</emphasis> new variables save in the
global space, prepend the function content with a <literal>*</literal>. This will
have the same effect as replacing all <literal>=</literal> signs in the function
with the <literal>*</literal> operator.</para>
      <para>Remember that your file is also a function, just without the curly
brackets. This means that when working on the top level of your program,
<literal>args</literal> actually refer to the arguments specified on the command
line. All arguments are strings, but built-in functions that can convert
them to numbers exist.</para>
      <para>The previous example functions did not have any return values. This is
merely because they didn't need such things. To define a return value,
the return value must be sent to the special variable <literal>return</literal>.</para>
      <screen>{/a,b/a b ! multiply = return;} = 2mul;
33 3 ! 2mul = 2mult;
stdout 2mult ! write;
</screen>
      <para>The execution of a function does <emphasis role="bold"><emphasis>not</emphasis></emphasis> stop when a value
is assigned to <literal>return</literal>. This has both advantages and
disadvantages.</para>
      <para>Many things are almost impossible to do without the built-in
functions. Some are completely impossible. See <xref linkend="Built-In"></xref>. As all
objects in Enigma are pointers, several built-in functions actually
modify the objects sent to them as arguments. To solve this problem, one
must use the <literal>clone</literal> function.</para>
    </sect1>

    <sect1 label="2.8" id="Conditionals">
      <title>Conditionals</title>
      <para>Any value can be related to another value. 78 is less than 85. 2 equals
2. "Hi" is not "Bye". Enigma comes with a basic set of functions that
can be used to test these relations. The functions <literal>greater</literal>,
<literal>lesser</literal>, <literal>equal</literal>, <literal>not</literal>, <literal>or</literal> and <literal>and</literal> are
available. These functions return either true or false. To run a
function on the condition that a relational function has returned true,
use the function <literal>act</literal>.</para>
      <para>While <literal>lesser</literal> and <literal>greater</literal> are aimed at numbers only,
and <literal>and</literal>, <literal>or</literal> and <literal>not</literal> are aimed at booleans only,
<literal>equal</literal> can be used on all objects. It tests for all equalities.</para>
      <screen>2 = a;
4 = b;

a 2 ! add | temp b ! equal = cond1;
"47" ! num | temp 48 ! greater = cond2;

cond1 cond2 ! and | temp write stdout "4 = 4 and 47 &gt; 48\n" ! act;
cond1 cond2 ! or | temp write stdout "4 = 4 or 47 &gt; 48\n" ! act;
cond2 ! not | cond1 temp ! and | temp write stdout "4 = 4 and !(47 &gt;
48)\n" ! act;
</screen>
      <para>Even simpler, one can do this (though there's no real need for it):</para>
      <screen># Instead of stdout "Hello" !write;
true write stdout "Hello" !act;
</screen>
    </sect1>

    <sect1 label="2.9" id="Loops">
      <title>Loops</title>
      <para>There are several ways to loop pieces of code in Enigma. One can create
a function that calls itself, for example. It is, however, advised to
use the <literal>loop</literal> function.</para>
      <screen># Infinite loop
{stdout "Forever\n" ! write; true = return;} ! loop;
</screen>
      <para><literal>loop</literal> works a bit like <literal>act</literal>, except that it runs on the
premise of the return value of the function it calls. If it returns
true, or any other value that can be considered true (non-zero numbers,
non-empty strings, files, etc.), it runs the function again. If it
returns false, the loop stops. It naturally runs the first time no
matter what (no return value has been created yet).</para>
    </sect1>

    <sect1 label="2.10" id="Undefined">
      <title>Undefined behaviour</title>
      <para>Enigma is still new. The way built-in functions act, the way error
messages appear, and the way some odd details of the language works are
still undefined. In general, when something seems likely to work, it
will work. But it's not necessarily defined to work.</para>
    </sect1>
  </chapter>

  <chapter label="3" id="Future">
    <title>Future aspects</title>
    <para>As Enigma is right now, it is quite limited. The only way that it can
interact with the rest of one's system is by reading and writing files
and by executing shell commands using the <literal>system</literal> built-in
function. This obviously needs to be improved. A foreign function
interface system must be implemented in version 0.2. It should be
possible for Enigma to do everything C can.</para>
    <para>The number of built-in functions seems reasonable, but it may be a good
idea to implement a few more. These eventual functions should be focused
on making things easier. Specifically, an import function should be
considered. It is possible to create an import function in Enigma
directly, but it's not exactly fast. Introducing a &ldquo;compile&rdquo; function
should solve that.</para>
  </chapter>

  <chapter label="4" id="Implementations">
    <title>Implementations</title>
    <para><indexterm role="pg"><primary>enigma</primary></indexterm>As of right now (beginning of June 2010) there is only one
implementation. It is written in Java and is called enigma (with a
lowercase e). The code is bulky and was not written by an experienced
Java hacker. For v0.2 it may be a good idea to write the interpreter in
C instead. Implementing a foreign function interface should be easier
that way.</para>
    <para>The current implementation can be downloaded at
<ulink url="http://metanohi.org/projects/enigma">http://metanohi.org/projects/enigma</ulink>.</para>
  </chapter>

  <chapter label="5" id="Comparison">
    <title>Comparison with other languages</title>
    <sect1 label="5.1" id="Compared-assigning">
      <title>Assigning values</title>
      <blockquote>
        <para><emphasis role="bold">C:</emphasis></para>
        <screen>
type var = value;
</screen>
      </blockquote>
      <blockquote>
        <para><emphasis role="bold">Python:</emphasis></para>
        <screen>
var = value
</screen>
      </blockquote>
      <blockquote>
        <para><emphasis role="bold">Enigma:</emphasis></para>
        <screen>
value = var;
</screen>
      </blockquote>
    </sect1>

    <sect1 label="5.2" id="Compared-conditionals">
      <title>Conditionals</title>
      <blockquote>
        <para><emphasis role="bold">C:</emphasis></para>
        <screen>
if ((a == 2 &amp;&amp; b &lt; 5) || (c != 4 &amp;&amp; !d)) do_something();
</screen>
      </blockquote>
      <blockquote>
        <para><emphasis role="bold">Python:</emphasis></para>
        <screen>
if (a == 2 and b &lt; 5) or (c != 4 and not d):
do_something()
</screen>
      </blockquote>
      <blockquote>
        <para><emphasis role="bold">Enigma:</emphasis></para>
        <screen>
a 2 ! equal = cond-a;
b 5 ! lesser = cond-b;
c 4 ! equal ! not = cond-c;
d ! not = cond-d;
cond-a cond-b ! and = ncond-ab;
cond-c cond-d ! and = ncond-cd;
ncond-ab ncond-cd ! or = actcond;
actcond do-something ! act;
</screen>
      </blockquote>
    </sect1>

    <sect1 label="5.3" id="Compared-looping">
      <title>Looping</title>
      <blockquote>
        <para><emphasis role="bold">C:</emphasis></para>
        <screen>
while (thinking) run();

for (int i = 0; i &lt; 18; i++) run(i);
</screen>
      </blockquote>
      <blockquote>
        <para><emphasis role="bold">Python:</emphasis></para>
        <screen>
while thinking: run()

for i in range(18): run(i)
</screen>
      </blockquote>
      <blockquote>
        <para><emphasis role="bold">Enigma:</emphasis></para>
        <screen>{!run; thinking ! clone = return;} ! loop;

0 = i;
{i ! run; i 1 ! add; i 18 ! equal = return;} ! loop;
</screen>
      </blockquote>
    </sect1>

    <sect1 label="5.4" id="Compared-functions">
      <title>Functions</title>
      <blockquote>
        <para><emphasis role="bold">C:</emphasis></para>
        <screen>int time(float space) {
    return (int) space / 3;
}

t = time(81.65);
</screen>
      </blockquote>
      <blockquote>
        <para><emphasis role="bold">Python:</emphasis></para>
        <screen>
def time(space):
    return int(space / 3)

t = time(81.65)
</screen>
      </blockquote>
      <blockquote>
        <para><emphasis role="bold">Enigma:</emphasis></para>
        <screen>{/space/space 3 ! divide ! clone ! round = return;} = time;

81.65 ! time = t;
</screen>
      </blockquote>
    </sect1>
  </chapter>

  <chapter label="6" id="Built-In">
    <title>Built-in values and functions</title>
    <sect1 label="6.1" id="Built-In-values">
      <title>Values</title>
      <para><indexterm role="cp"><primary>built-in values</primary></indexterm>The following variables are special and can be accessed anytime. They can
even be overwritten.</para>
      <screen>args, return, temp, stdin, stderr, stdout, zero, true, false, none, @pi,
@e, cwd, cpd, fnm
</screen>
      <para><literal>zero</literal> is a fake writable file that does nothing. <literal>none</literal> is an
abstract variable with an internal value of.. none. <literal>@pi</literal> is
Pi. <literal>@e</literal> is Euler's number. <literal>cwd</literal> is the directory from which
Enigma is run, <literal>cpd</literal> is the directory in which the current program
file resides, and <literal>fnm</literal> is the filename of the current program
file. The rest are self-explanatory &mdash; and <literal>args</literal>, <literal>return</literal>
and <literal>temp</literal> are extra special.</para>
    </sect1>

    <sect1 label="6.2" id="Built-In-functions">
      <title>Functions</title>
      <para><indexterm role="cp"><primary>built-in functions</primary></indexterm>Enigma has few built-in functions. But they do exist.</para>
      <para role="continues"><literal>str(OBJECT...)</literal>: Converts all supplied values to strings.</para>
      <para role="continues"><literal>num(OBJECT...)</literal>: Converts all supplied values to numbers.</para>
      <para role="continues"><literal>list(OBJECT...)</literal>: Puts all supplied values in a list and destroys
nested lists at one level.</para>
      <para role="continues"><literal>bool(OBJECT...)</literal>: Converts all supplied values to booleans.</para>
      <para role="continues"><literal>code(OBJECT...)</literal>: Converts all supplied values to code strings.</para>
      <para role="continues"><literal>repr(OBJECT...)</literal>: Converts all supplied values to representational
strings. Strings get prepended and appended by " characters, code
objects are surrounded by { and }, and so on.</para>
      <para role="continues"><literal>type(OBJECT...)</literal>: Converts all supplied values to type strings
(string, number, file, etc.).</para>
      <para role="continues"><literal>len(OBJECT...)</literal>: Converts all supplied values to their length. This
can be used for both strings and lists.</para>
      <para role="continues"><literal>clone(OBJECT...)</literal>: Clones all supplied values. When an object is
cloned, its value is assigned to a new variable. The list of clones is
returned.</para>
      <para role="continues"><literal>slice(LIST|STRING, NUMBER, NUMBER)</literal>: Returns a list value sliced
according to the first and second number if the first variable is a
list variable, or a substring if the first variable is a string
variable.</para>
      <para role="continues"><literal>loop(FUNCTION, [OBJECT]...)</literal>: Executes function until it returns
false. Sends the rest of the specified variables (if any) to the
function as arguments.</para>
      <para role="continues"><literal>open(STRING, STRING)</literal>: Opens the file by the name of the first
string, using the second string as its guide as to how it should be
opened. "r" means to read, "w" means to write, and "a" means to
append. Returns a file object.</para>
      <para role="continues"><literal>close(FILE...)</literal>: Closes files.</para>
      <para role="continues"><literal>read(FILE)</literal>: Reads one character of a file and returns it. If no
more characters are present, an empty string is returned.</para>
      <para role="continues"><literal>write(FILE, STRING)</literal>: Writes a string to a file.</para>
      <para role="continues"><literal>greater(NUMBER, NUMBER...</literal>: Checks if the first number is
greater than the rest and returns true or false.</para>
      <para role="continues"><literal>lesser(NUMBER, NUMBER...</literal>: Checks if the first number is
lesser than the rest and returns true or false.</para>
      <para role="continues"><literal>equal(OBJECT, OBJECT...</literal>: Checks if the objects are equal and returns
true or false.</para>
      <para role="continues"><literal>and(BOOLEAN...)</literal>: Checks if all booleans are true and returns true
or false.</para>
      <para role="continues"><literal>or(BOOLEAN...)</literal>: Checks if at least one boolean is true and returns
true or false.</para>
      <para role="continues"><literal>not(BOOLEAN...)</literal>: Converts values of true to values of false, and
vice-versa.</para>
      <para role="continues"><literal>act(BOOLEAN, FUNCTION, [OBJECT]...)</literal>: Run the function with the
optional objects as arguments if the boolean is true.</para>
      <para role="continues"><literal>system(STRING...)</literal>: Join the strings and run the result as a
system command.</para>
      <para role="continues"><literal>add(NUMBER|STRING|CODE|LIST...)</literal>: Add objects together. Numbers, strings, code
strings and lists can be used, but only with similar types. The type
of the first object determines what types the rest must be. The result
is stored in the first object and also returned.</para>
      <para role="continues"><literal>subtract(NUMBER...)</literal>: Subtract numbers from each other. The
first object receives the final number. It is also returned.</para>
      <para role="continues"><literal>multiply(NUMBER...)</literal>: Multiply numbers with each other. The
first object receives the final number. It is also returned.</para>
      <para role="continues"><literal>divide(NUMBER...)</literal>: Divide numbers with each other. The
first object receives the final number. It is also returned.</para>
      <para role="continues"><literal>mod(NUMBER, NUMBER)</literal>: Finds the remainder of the first number
divided with the second number and returns it as a new variable.</para>
      <para role="continues"><literal>pow(NUMBER, NUMBER)</literal>: Returns first number^second number.</para>
      <para role="continues"><literal>log(NUMBER, [NUMBER])</literal>: Returns the logarithm of the first
number. If the second number is not specified, the natural logarith is
used.</para>
      <para role="continues"><literal>random()</literal>: Returns a random number between 0 and 1.</para>
      <para role="continues"><literal>abs(NUMBER...)</literal>: Sets and returns absolute values of numbers.</para>
      <para role="continues"><literal>round(NUMBER, NUMBER)</literal>: Rounds the first number with x decimals,
where x is the second number.</para>
      <para role="continues"><literal>floor(NUMBER, NUMBER)</literal>: Floors the first number with x decimals,
where x is the second number.</para>
      <para role="continues"><literal>ceil(NUMBER, NUMBER)</literal>: "Ceils" the first number with x decimals,
where x is the second number.</para>
      <para role="continues"><literal>sin(NUMBER...)</literal>: Sets and returns sine values.</para>
      <para role="continues"><literal>cos(NUMBER...)</literal>: Sets and returns cosine values.</para>
      <para role="continues"><literal>tan(NUMBER...)</literal>: Sets and returns tangent values.</para>
      <para role="continues"><literal>asin(NUMBER...)</literal>: Sets and returns arcsine values.</para>
      <para role="continues"><literal>acos(NUMBER...)</literal>: Sets and returns arccosine values.</para>
      <para role="continues"><literal>atan(NUMBER...)</literal>: Sets and returns arctangent values.</para>
      <para role="continues"><literal>sinh(NUMBER...)</literal>: Sets and returns hyperbolic sine values.</para>
      <para role="continues"><literal>cosh(NUMBER...)</literal>: Sets and returns hyperbolic cosine values.</para>
      <para role="continues"><literal>tanh(NUMBER...)</literal>: Sets and returns hyperbolic tangent values.</para>
    </sect1>
  </chapter>

  <appendix id="Copying-This-Manual">
    <title>GNU Free Documentation License</title>
<!-- The GNU Free Documentation License. -->
    <para>Version 1.3, 3 November 2008
<!-- This file is intended to be included within another document, -->
<!-- hence no sectioning command or @node. --><literallayout>
Copyright &copy; 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc.
<ulink url="http://fsf.org/">http://fsf.org/</ulink>

Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
</literallayout></para>
    <orderedlist numeration="arabic" role="0">
      <listitem>
        <para>PREAMBLE</para>
        <para>The purpose of this License is to make a manual, textbook, or other
functional and useful document <firstterm>free</firstterm> in the sense of freedom: to
assure everyone the effective freedom to copy and redistribute it,
with or without modifying it, either commercially or noncommercially.
Secondarily, this License preserves for the author and publisher a way
to get credit for their work, while not being considered responsible
for modifications made by others.</para>
        <para>This License is a kind of &ldquo;copyleft&rdquo;, which means that derivative
works of the document must themselves be free in the same sense.  It
complements the GNU General Public License, which is a copyleft
license designed for free software.</para>
        <para>We have designed this License in order to use it for manuals for free
software, because free software needs free documentation: a free
program should come with manuals providing the same freedoms that the
software does.  But this License is not limited to software manuals;
it can be used for any textual work, regardless of subject matter or
whether it is published as a printed book.  We recommend this License
principally for works whose purpose is instruction or reference.</para>
      </listitem>
      <listitem>
        <para>APPLICABILITY AND DEFINITIONS</para>
        <para>This License applies to any manual or other work, in any medium, that
contains a notice placed by the copyright holder saying it can be
distributed under the terms of this License.  Such a notice grants a
world-wide, royalty-free license, unlimited in duration, to use that
work under the conditions stated herein.  The &ldquo;Document&rdquo;, below,
refers to any such manual or work.  Any member of the public is a
licensee, and is addressed as &ldquo;you&rdquo;.  You accept the license if you
copy, modify or distribute the work in a way requiring permission
under copyright law.</para>
        <para>A &ldquo;Modified Version&rdquo; of the Document means any work containing the
Document or a portion of it, either copied verbatim, or with
modifications and/or translated into another language.</para>
        <para>A &ldquo;Secondary Section&rdquo; is a named appendix or a front-matter section
of the Document that deals exclusively with the relationship of the
publishers or authors of the Document to the Document's overall
subject (or to related matters) and contains nothing that could fall
directly within that overall subject.  (Thus, if the Document is in
part a textbook of mathematics, a Secondary Section may not explain
any mathematics.)  The relationship could be a matter of historical
connection with the subject or with related matters, or of legal,
commercial, philosophical, ethical or political position regarding
them.</para>
        <para>The &ldquo;Invariant Sections&rdquo; are certain Secondary Sections whose titles
are designated, as being those of Invariant Sections, in the notice
that says that the Document is released under this License.  If a
section does not fit the above definition of Secondary then it is not
allowed to be designated as Invariant.  The Document may contain zero
Invariant Sections.  If the Document does not identify any Invariant
Sections then there are none.</para>
        <para>The &ldquo;Cover Texts&rdquo; are certain short passages of text that are listed,
as Front-Cover Texts or Back-Cover Texts, in the notice that says that
the Document is released under this License.  A Front-Cover Text may
be at most 5 words, and a Back-Cover Text may be at most 25 words.</para>
        <para>A &ldquo;Transparent&rdquo; copy of the Document means a machine-readable copy,
represented in a format whose specification is available to the
general public, that is suitable for revising the document
straightforwardly with generic text editors or (for images composed of
pixels) generic paint programs or (for drawings) some widely available
drawing editor, and that is suitable for input to text formatters or
for automatic translation to a variety of formats suitable for input
to text formatters.  A copy made in an otherwise Transparent file
format whose markup, or absence of markup, has been arranged to thwart
or discourage subsequent modification by readers is not Transparent.
An image format is not Transparent if used for any substantial amount
of text.  A copy that is not &ldquo;Transparent&rdquo; is called &ldquo;Opaque&rdquo;.</para>
        <para>Examples of suitable formats for Transparent copies include plain
ascii without markup, Texinfo input format, La&tex; input
format, <acronym>SGML</acronym> or <acronym>XML</acronym> using a publicly available
<acronym>DTD</acronym>, and standard-conforming simple <acronym>HTML</acronym>,
PostScript or <acronym>PDF</acronym> designed for human modification.  Examples
of transparent image formats include <acronym>PNG</acronym>, <acronym>XCF</acronym> and
<acronym>JPG</acronym>.  Opaque formats include proprietary formats that can be
read and edited only by proprietary word processors, <acronym>SGML</acronym> or
<acronym>XML</acronym> for which the <acronym>DTD</acronym> and/or processing tools are
not generally available, and the machine-generated <acronym>HTML</acronym>,
PostScript or <acronym>PDF</acronym> produced by some word processors for
output purposes only.</para>
        <para>The &ldquo;Title Page&rdquo; means, for a printed book, the title page itself,
plus such following pages as are needed to hold, legibly, the material
this License requires to appear in the title page.  For works in
formats which do not have any title page as such, &ldquo;Title Page&rdquo; means
the text near the most prominent appearance of the work's title,
preceding the beginning of the body of the text.</para>
        <para>The &ldquo;publisher&rdquo; means any person or entity that distributes copies
of the Document to the public.</para>
        <para>A section &ldquo;Entitled XYZ&rdquo; means a named subunit of the Document whose
title either is precisely XYZ or contains XYZ in parentheses following
text that translates XYZ in another language.  (Here XYZ stands for a
specific section name mentioned below, such as &ldquo;Acknowledgements&rdquo;,
&ldquo;Dedications&rdquo;, &ldquo;Endorsements&rdquo;, or &ldquo;History&rdquo;.)  To &ldquo;Preserve the Title&rdquo;
of such a section when you modify the Document means that it remains a
section &ldquo;Entitled XYZ&rdquo; according to this definition.</para>
        <para>The Document may include Warranty Disclaimers next to the notice which
states that this License applies to the Document.  These Warranty
Disclaimers are considered to be included by reference in this
License, but only as regards disclaiming warranties: any other
implication that these Warranty Disclaimers may have is void and has
no effect on the meaning of this License.</para>
      </listitem>
      <listitem>
        <para>VERBATIM COPYING</para>
        <para>You may copy and distribute the Document in any medium, either
commercially or noncommercially, provided that this License, the
copyright notices, and the license notice saying this License applies
to the Document are reproduced in all copies, and that you add no other
conditions whatsoever to those of this License.  You may not use
technical measures to obstruct or control the reading or further
copying of the copies you make or distribute.  However, you may accept
compensation in exchange for copies.  If you distribute a large enough
number of copies you must also follow the conditions in section 3.</para>
        <para>You may also lend copies, under the same conditions stated above, and
you may publicly display copies.</para>
      </listitem>
      <listitem>
        <para>COPYING IN QUANTITY</para>
        <para>If you publish printed copies (or copies in media that commonly have
printed covers) of the Document, numbering more than 100, and the
Document's license notice requires Cover Texts, you must enclose the
copies in covers that carry, clearly and legibly, all these Cover
Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on
the back cover.  Both covers must also clearly and legibly identify
you as the publisher of these copies.  The front cover must present
the full title with all words of the title equally prominent and
visible.  You may add other material on the covers in addition.
Copying with changes limited to the covers, as long as they preserve
the title of the Document and satisfy these conditions, can be treated
as verbatim copying in other respects.</para>
        <para>If the required texts for either cover are too voluminous to fit
legibly, you should put the first ones listed (as many as fit
reasonably) on the actual cover, and continue the rest onto adjacent
pages.</para>
        <para>If you publish or distribute Opaque copies of the Document numbering
more than 100, you must either include a machine-readable Transparent
copy along with each Opaque copy, or state in or with each Opaque copy
a computer-network location from which the general network-using
public has access to download using public-standard network protocols
a complete Transparent copy of the Document, free of added material.
If you use the latter option, you must take reasonably prudent steps,
when you begin distribution of Opaque copies in quantity, to ensure
that this Transparent copy will remain thus accessible at the stated
location until at least one year after the last time you distribute an
Opaque copy (directly or through your agents or retailers) of that
edition to the public.</para>
        <para>It is requested, but not required, that you contact the authors of the
Document well before redistributing any large number of copies, to give
them a chance to provide you with an updated version of the Document.</para>
      </listitem>
      <listitem>
        <para>MODIFICATIONS</para>
        <para>You may copy and distribute a Modified Version of the Document under
the conditions of sections 2 and 3 above, provided that you release
the Modified Version under precisely this License, with the Modified
Version filling the role of the Document, thus licensing distribution
and modification of the Modified Version to whoever possesses a copy
of it.  In addition, you must do these things in the Modified Version:</para>
        <orderedlist numeration="upperalpha">
          <listitem>
            <para>Use in the Title Page (and on the covers, if any) a title distinct
from that of the Document, and from those of previous versions
(which should, if there were any, be listed in the History section
of the Document).  You may use the same title as a previous version
if the original publisher of that version gives permission.</para>
          </listitem>
          <listitem>
            <para>List on the Title Page, as authors, one or more persons or entities
responsible for authorship of the modifications in the Modified
Version, together with at least five of the principal authors of the
Document (all of its principal authors, if it has fewer than five),
unless they release you from this requirement.</para>
          </listitem>
          <listitem>
            <para>State on the Title page the name of the publisher of the
Modified Version, as the publisher.</para>
          </listitem>
          <listitem>
            <para>Preserve all the copyright notices of the Document.</para>
          </listitem>
          <listitem>
            <para>Add an appropriate copyright notice for your modifications
adjacent to the other copyright notices.</para>
          </listitem>
          <listitem>
            <para>Include, immediately after the copyright notices, a license notice
giving the public permission to use the Modified Version under the
terms of this License, in the form shown in the Addendum below.</para>
          </listitem>
          <listitem>
            <para>Preserve in that license notice the full lists of Invariant Sections
and required Cover Texts given in the Document's license notice.</para>
          </listitem>
          <listitem>
            <para>Include an unaltered copy of this License.</para>
          </listitem>
          <listitem>
            <para>Preserve the section Entitled &ldquo;History&rdquo;, Preserve its Title, and add
to it an item stating at least the title, year, new authors, and
publisher of the Modified Version as given on the Title Page.  If
there is no section Entitled &ldquo;History&rdquo; in the Document, create one
stating the title, year, authors, and publisher of the Document as
given on its Title Page, then add an item describing the Modified
Version as stated in the previous sentence.</para>
          </listitem>
          <listitem>
            <para>Preserve the network location, if any, given in the Document for
public access to a Transparent copy of the Document, and likewise
the network locations given in the Document for previous versions
it was based on.  These may be placed in the &ldquo;History&rdquo; section.
You may omit a network location for a work that was published at
least four years before the Document itself, or if the original
publisher of the version it refers to gives permission.</para>
          </listitem>
          <listitem>
            <para>For any section Entitled &ldquo;Acknowledgements&rdquo; or &ldquo;Dedications&rdquo;, Preserve
the Title of the section, and preserve in the section all the
substance and tone of each of the contributor acknowledgements and/or
dedications given therein.</para>
          </listitem>
          <listitem>
            <para>Preserve all the Invariant Sections of the Document,
unaltered in their text and in their titles.  Section numbers
or the equivalent are not considered part of the section titles.</para>
          </listitem>
          <listitem>
            <para>Delete any section Entitled &ldquo;Endorsements&rdquo;.  Such a section
may not be included in the Modified Version.</para>
          </listitem>
          <listitem>
            <para>Do not retitle any existing section to be Entitled &ldquo;Endorsements&rdquo; or
to conflict in title with any Invariant Section.</para>
          </listitem>
          <listitem>
            <para>Preserve any Warranty Disclaimers.</para>
          </listitem>
        </orderedlist>
        <para>If the Modified Version includes new front-matter sections or
appendices that qualify as Secondary Sections and contain no material
copied from the Document, you may at your option designate some or all
of these sections as invariant.  To do this, add their titles to the
list of Invariant Sections in the Modified Version's license notice.
These titles must be distinct from any other section titles.</para>
        <para>You may add a section Entitled &ldquo;Endorsements&rdquo;, provided it contains
nothing but endorsements of your Modified Version by various
parties&mdash;for example, statements of peer review or that the text has
been approved by an organization as the authoritative definition of a
standard.</para>
        <para>You may add a passage of up to five words as a Front-Cover Text, and a
passage of up to 25 words as a Back-Cover Text, to the end of the list
of Cover Texts in the Modified Version.  Only one passage of
Front-Cover Text and one of Back-Cover Text may be added by (or
through arrangements made by) any one entity.  If the Document already
includes a cover text for the same cover, previously added by you or
by arrangement made by the same entity you are acting on behalf of,
you may not add another; but you may replace the old one, on explicit
permission from the previous publisher that added the old one.</para>
        <para>The author(s) and publisher(s) of the Document do not by this License
give permission to use their names for publicity for or to assert or
imply endorsement of any Modified Version.</para>
      </listitem>
      <listitem>
        <para>COMBINING DOCUMENTS</para>
        <para>You may combine the Document with other documents released under this
License, under the terms defined in section 4 above for modified
versions, provided that you include in the combination all of the
Invariant Sections of all of the original documents, unmodified, and
list them all as Invariant Sections of your combined work in its
license notice, and that you preserve all their Warranty Disclaimers.</para>
        <para>The combined work need only contain one copy of this License, and
multiple identical Invariant Sections may be replaced with a single
copy.  If there are multiple Invariant Sections with the same name but
different contents, make the title of each such section unique by
adding at the end of it, in parentheses, the name of the original
author or publisher of that section if known, or else a unique number.
Make the same adjustment to the section titles in the list of
Invariant Sections in the license notice of the combined work.</para>
        <para>In the combination, you must combine any sections Entitled &ldquo;History&rdquo;
in the various original documents, forming one section Entitled
&ldquo;History&rdquo;; likewise combine any sections Entitled &ldquo;Acknowledgements&rdquo;,
and any sections Entitled &ldquo;Dedications&rdquo;.  You must delete all
sections Entitled &ldquo;Endorsements.&rdquo;</para>
      </listitem>
      <listitem>
        <para>COLLECTIONS OF DOCUMENTS</para>
        <para>You may make a collection consisting of the Document and other documents
released under this License, and replace the individual copies of this
License in the various documents with a single copy that is included in
the collection, provided that you follow the rules of this License for
verbatim copying of each of the documents in all other respects.</para>
        <para>You may extract a single document from such a collection, and distribute
it individually under this License, provided you insert a copy of this
License into the extracted document, and follow this License in all
other respects regarding verbatim copying of that document.</para>
      </listitem>
      <listitem>
        <para>AGGREGATION WITH INDEPENDENT WORKS</para>
        <para>A compilation of the Document or its derivatives with other separate
and independent documents or works, in or on a volume of a storage or
distribution medium, is called an &ldquo;aggregate&rdquo; if the copyright
resulting from the compilation is not used to limit the legal rights
of the compilation's users beyond what the individual works permit.
When the Document is included in an aggregate, this License does not
apply to the other works in the aggregate which are not themselves
derivative works of the Document.</para>
        <para>If the Cover Text requirement of section 3 is applicable to these
copies of the Document, then if the Document is less than one half of
the entire aggregate, the Document's Cover Texts may be placed on
covers that bracket the Document within the aggregate, or the
electronic equivalent of covers if the Document is in electronic form.
Otherwise they must appear on printed covers that bracket the whole
aggregate.</para>
      </listitem>
      <listitem>
        <para>TRANSLATION</para>
        <para>Translation is considered a kind of modification, so you may
distribute translations of the Document under the terms of section 4.
Replacing Invariant Sections with translations requires special
permission from their copyright holders, but you may include
translations of some or all Invariant Sections in addition to the
original versions of these Invariant Sections.  You may include a
translation of this License, and all the license notices in the
Document, and any Warranty Disclaimers, provided that you also include
the original English version of this License and the original versions
of those notices and disclaimers.  In case of a disagreement between
the translation and the original version of this License or a notice
or disclaimer, the original version will prevail.</para>
        <para>If a section in the Document is Entitled &ldquo;Acknowledgements&rdquo;,
&ldquo;Dedications&rdquo;, or &ldquo;History&rdquo;, the requirement (section 4) to Preserve
its Title (section 1) will typically require changing the actual
title.</para>
      </listitem>
      <listitem>
        <para>TERMINATION</para>
        <para>You may not copy, modify, sublicense, or distribute the Document
except as expressly provided under this License.  Any attempt
otherwise to copy, modify, sublicense, or distribute it is void, and
will automatically terminate your rights under this License.</para>
        <para>However, if you cease all violation of this License, then your license
from a particular copyright holder is reinstated (a) provisionally,
unless and until the copyright holder explicitly and finally
terminates your license, and (b) permanently, if the copyright holder
fails to notify you of the violation by some reasonable means prior to
60 days after the cessation.</para>
        <para>Moreover, your license from a particular copyright holder is
reinstated permanently if the copyright holder notifies you of the
violation by some reasonable means, this is the first time you have
received notice of violation of this License (for any work) from that
copyright holder, and you cure the violation prior to 30 days after
your receipt of the notice.</para>
        <para>Termination of your rights under this section does not terminate the
licenses of parties who have received copies or rights from you under
this License.  If your rights have been terminated and not permanently
reinstated, receipt of a copy of some or all of the same material does
not give you any rights to use it.</para>
      </listitem>
      <listitem>
        <para>FUTURE REVISIONS OF THIS LICENSE</para>
        <para>The Free Software Foundation may publish new, revised versions
of the GNU Free Documentation License from time to time.  Such new
versions will be similar in spirit to the present version, but may
differ in detail to address new problems or concerns.  See
<ulink url="http://www.gnu.org/copyleft/">http://www.gnu.org/copyleft/</ulink>.</para>
        <para>Each version of the License is given a distinguishing version number.
If the Document specifies that a particular numbered version of this
License &ldquo;or any later version&rdquo; applies to it, you have the option of
following the terms and conditions either of that specified version or
of any later version that has been published (not as a draft) by the
Free Software Foundation.  If the Document does not specify a version
number of this License, you may choose any version ever published (not
as a draft) by the Free Software Foundation.  If the Document
specifies that a proxy can decide which future versions of this
License can be used, that proxy's public statement of acceptance of a
version permanently authorizes you to choose that version for the
Document.</para>
      </listitem>
      <listitem>
        <para>RELICENSING</para>
        <para>&ldquo;Massive Multiauthor Collaboration Site&rdquo; (or &ldquo;MMC Site&rdquo;) means any
World Wide Web server that publishes copyrightable works and also
provides prominent facilities for anybody to edit those works.  A
public wiki that anybody can edit is an example of such a server.  A
&ldquo;Massive Multiauthor Collaboration&rdquo; (or &ldquo;MMC&rdquo;) contained in the
site means any set of copyrightable works thus published on the MMC
site.</para>
        <para>&ldquo;CC-BY-SA&rdquo; means the Creative Commons Attribution-Share Alike 3.0
license published by Creative Commons Corporation, a not-for-profit
corporation with a principal place of business in San Francisco,
California, as well as future copyleft versions of that license
published by that same organization.</para>
        <para>&ldquo;Incorporate&rdquo; means to publish or republish a Document, in whole or
in part, as part of another Document.</para>
        <para>An MMC is &ldquo;eligible for relicensing&rdquo; if it is licensed under this
License, and if all works that were first published under this License
somewhere other than this MMC, and subsequently incorporated in whole
or in part into the MMC, (1) had no cover texts or invariant sections,
and (2) were thus incorporated prior to November 1, 2008.</para>
        <para>The operator of an MMC Site may republish an MMC contained in the site
under CC-BY-SA on the same site at any time before August 1, 2009,
provided the MMC is eligible for relicensing.</para>
      </listitem>
    </orderedlist>
    <bridgehead renderas="sect1">ADDENDUM: How to use this License for your documents</bridgehead>
    <para>To use this License in a document you have written, include a copy of
the License in the document and put the following copyright and
license notices just after the title page:</para>
    <screen>
  Copyright (C)  <replaceable>year</replaceable>  <replaceable>your name</replaceable>.
  Permission is granted to copy, distribute and/or modify this document
  under the terms of the GNU Free Documentation License, Version 1.3
  or any later version published by the Free Software Foundation;
  with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
  Texts.  A copy of the license is included in the section entitled ``GNU
  Free Documentation License''.
</screen>
    <para>If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts,
replace the &ldquo;with&hellip;Texts.&rdquo; line with this:</para>
    <screen>
    with the Invariant Sections being <replaceable>list their titles</replaceable>, with
    the Front-Cover Texts being <replaceable>list</replaceable>, and with the Back-Cover Texts
    being <replaceable>list</replaceable>.
</screen>
    <para>If you have Invariant Sections without Cover Texts, or some other
combination of the three, merge those two alternatives to suit the
situation.</para>
    <para>If your document contains nontrivial examples of program code, we
recommend releasing these examples in parallel under your choice of
free software license, such as the GNU General Public License,
to permit their use in free software.</para>
<!-- Local Variables: -->
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  </appendix>

  <chapter label="" xreflabel="Index" id="Index">
    <title>Index</title>
    <index></index>
  </chapter>
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