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<TITLE>CLN, a Class Library for Numbers: Introduction</TITLE>
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<A NAME="Introduction"></A>
<H1> 1. Introduction </H1>
<!--docid::SEC1::-->
<P>
CLN is a library for computations with all kinds of numbers.
It has a rich set of number classes:
</P>
<P>
<UL>
<LI>
Integers (with unlimited precision),
<P>
</P>
<LI>
Rational numbers,
<P>
</P>
<LI>
Floating-point numbers:
<P>
<UL>
<LI>
Short float,
<LI>
Single float,
<LI>
Double float,
<LI>
Long float (with unlimited precision),
</UL>
<P>
</P>
<LI>
Complex numbers,
<P>
</P>
<LI>
Modular integers (integers modulo a fixed integer),
<P>
</P>
<LI>
Univariate polynomials.
</UL>
<P>
The subtypes of the complex numbers among these are exactly the
types of numbers known to the Common Lisp language. Therefore
<CODE>CLN</CODE> can be used for Common Lisp implementations, giving
`<SAMP>CLN</SAMP>' another meaning: it becomes an abbreviation of
"Common Lisp Numbers".
</P>
<P>
The CLN package implements
</P>
<P>
<UL>
<LI>
Elementary functions (<CODE>+</CODE>, <CODE>-</CODE>, <CODE>*</CODE>, <CODE>/</CODE>, <CODE>sqrt</CODE>,
comparisons, <small>...</small>),
<P>
</P>
<LI>
Logical functions (logical <CODE>and</CODE>, <CODE>or</CODE>, <CODE>not</CODE>, <small>...</small>),
<P>
</P>
<LI>
Transcendental functions (exponential, logarithmic, trigonometric, hyperbolic
functions and their inverse functions).
</UL>
<P>
CLN is a C++ library. Using C++ as an implementation language provides
</P>
<P>
<UL>
<LI>
efficiency: it compiles to machine code,
<LI>
type safety: the C++ compiler knows about the number types and complains
if, for example, you try to assign a float to an integer variable.
<LI>
algebraic syntax: You can use the <CODE>+</CODE>, <CODE>-</CODE>, <CODE>*</CODE>, <CODE>=</CODE>,
<CODE>==</CODE>, <small>...</small> operators as in C or C++.
</UL>
<P>
CLN is memory efficient:
</P>
<P>
<UL>
<LI>
Small integers and short floats are immediate, not heap allocated.
<LI>
Heap-allocated memory is reclaimed through an automatic, non-interruptive
garbage collection.
</UL>
<P>
CLN is speed efficient:
</P>
<P>
<UL>
<LI>
The kernel of CLN has been written in assembly language for some CPUs
(<CODE>i386</CODE>, <CODE>m68k</CODE>, <CODE>sparc</CODE>, <CODE>mips</CODE>, <CODE>arm</CODE>).
<LI>
<A NAME="IDX1"></A>
On all CPUs, CLN may be configured to use the superefficient low-level
routines from GNU GMP version 3.
<LI>
It uses Karatsuba multiplication, which is significantly faster
for large numbers than the standard multiplication algorithm.
<LI>
For very large numbers (more than 12000 decimal digits), it uses
Schnhage-Strassen
<A NAME="IDX2"></A>
multiplication, which is an asymptotically optimal multiplication
algorithm, for multiplication, division and radix conversion.
</UL>
<P>
CLN aims at being easily integrated into larger software packages:
</P>
<P>
<UL>
<LI>
The garbage collection imposes no burden on the main application.
<LI>
The library provides hooks for memory allocation and exceptions.
<LI>
<A NAME="IDX3"></A>
All non-macro identifiers are hidden in namespace <CODE>cln</CODE> in
order to avoid name clashes.
</UL>
<P>
<A NAME="Installation"></A>
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