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<TITLE>CLN, a Class Library for Numbers - 1. Introduction</TITLE>
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<H1><A NAME="SEC1" HREF="cln_toc.html#TOC1">1. Introduction</A></H1>

<P>
CLN is a library for computations with all kinds of numbers.
It has a rich set of number classes:


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Integers (with unlimited precision),

<LI>

Rational numbers,

<LI>

Floating-point numbers:


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Short float,
<LI>

Single float,
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Double float,
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Long float (with unlimited precision),
</UL>

<LI>

Complex numbers,

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Modular integers (integers modulo a fixed integer),

<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>
The CLN package implements


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Elementary functions (<CODE>+</CODE>, <CODE>-</CODE>, <CODE>*</CODE>, <CODE>/</CODE>, <CODE>sqrt</CODE>,
comparisons, ...),

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Logical functions (logical <CODE>and</CODE>, <CODE>or</CODE>, <CODE>not</CODE>, ...),

<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


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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>, ... operators as in C or C++.
</UL>

<P>
CLN is memory efficient:


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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:


<UL>
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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>

On all CPUs, CLN uses the superefficient low-level routines from GNU
GMP version 2.
<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
Sch�nhage-Strassen
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:


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<LI>

The garbage collection imposes no burden on the main application.
<LI>

The library provides hooks for memory allocation and exceptions.
</UL>

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