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163 lines
4.8 KiB
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<!-- Created by texi2html 1.56k from cln.texi on 5 May 2000 -->
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<TITLE>CLN, a Class Library for Numbers - 10. Internals</TITLE>
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Go to the <A HREF="cln_1.html">first</A>, <A HREF="cln_9.html">previous</A>, <A HREF="cln_11.html">next</A>, <A HREF="cln_13.html">last</A> section, <A HREF="cln_toc.html">table of contents</A>.
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<P><HR><P>
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<H1><A NAME="SEC59" HREF="cln_toc.html#TOC59">10. Internals</A></H1>
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<H2><A NAME="SEC60" HREF="cln_toc.html#TOC60">10.1 Why C++ ?</A></H2>
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<P>
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<A NAME="IDX313"></A>
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<P>
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Using C++ as an implementation language provides
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<UL>
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<LI>
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Efficiency: It compiles to machine code.
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<LI>
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<A NAME="IDX314"></A>
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Portability: It runs on all platforms supporting a C++ compiler. Because
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of the availability of GNU C++, this includes all currently used 32-bit and
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64-bit platforms, independently of the quality of the vendor's C++ compiler.
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<LI>
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Type safety: The C++ compilers knows about the number types and complains if,
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for example, you try to assign a float to an integer variable. However,
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a drawback is that C++ doesn't know about generic types, hence a restriction
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like that <CODE>operator+ (const cl_MI&, const cl_MI&)</CODE> requires that both
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arguments belong to the same modular ring cannot be expressed as a compile-time
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information.
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<LI>
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Algebraic syntax: The elementary operations <CODE>+</CODE>, <CODE>-</CODE>, <CODE>*</CODE>,
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<CODE>=</CODE>, <CODE>==</CODE>, ... can be used in infix notation, which is more
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convenient than Lisp notation <SAMP>`(+ x y)'</SAMP> or C notation <SAMP>`add(x,y,&z)'</SAMP>.
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</UL>
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<P>
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With these language features, there is no need for two separate languages,
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one for the implementation of the library and one in which the library's users
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can program. This means that a prototype implementation of an algorithm
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can be integrated into the library immediately after it has been tested and
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debugged. No need to rewrite it in a low-level language after having prototyped
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in a high-level language.
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<H2><A NAME="SEC61" HREF="cln_toc.html#TOC61">10.2 Memory efficiency</A></H2>
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<P>
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In order to save memory allocations, CLN implements:
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<LI>
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Object sharing: An operation like <CODE>x+0</CODE> returns <CODE>x</CODE> without copying
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it.
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<LI>
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<A NAME="IDX315"></A>
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<A NAME="IDX316"></A>
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Garbage collection: A reference counting mechanism makes sure that any
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number object's storage is freed immediately when the last reference to the
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object is gone.
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<LI>
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Small integers are represented as immediate values instead of pointers
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to heap allocated storage. This means that integers <CODE>> -2^29</CODE>,
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<CODE>< 2^29</CODE> don't consume heap memory, unless they were explicitly allocated
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on the heap.
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</UL>
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<H2><A NAME="SEC62" HREF="cln_toc.html#TOC62">10.3 Speed efficiency</A></H2>
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<P>
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Speed efficiency is obtained by the combination of the following tricks
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and algorithms:
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<LI>
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Small integers, being represented as immediate values, don't require
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memory access, just a couple of instructions for each elementary operation.
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<LI>
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The kernel of CLN has been written in assembly language for some CPUs
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(<CODE>i386</CODE>, <CODE>m68k</CODE>, <CODE>sparc</CODE>, <CODE>mips</CODE>, <CODE>arm</CODE>).
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<LI>
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On all CPUs, CLN may be configured to use the superefficient low-level
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routines from GNU GMP version 3.
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<LI>
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For large numbers, CLN uses, instead of the standard <CODE>O(N^2)</CODE>
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algorithm, the Karatsuba multiplication, which is an
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<CODE>O(N^1.6)</CODE>
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algorithm.
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<LI>
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For very large numbers (more than 12000 decimal digits), CLN uses
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Schönhage-Strassen
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<A NAME="IDX317"></A>
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multiplication, which is an asymptotically optimal multiplication
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algorithm.
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<LI>
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These fast multiplication algorithms also give improvements in the speed
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of division and radix conversion.
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</UL>
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<H2><A NAME="SEC63" HREF="cln_toc.html#TOC63">10.4 Garbage collection</A></H2>
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<P>
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<A NAME="IDX318"></A>
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<P>
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All the number classes are reference count classes: They only contain a pointer
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to an object in the heap. Upon construction, assignment and destruction of
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number objects, only the objects' reference count are manipulated.
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<P>
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Memory occupied by number objects are automatically reclaimed as soon as
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their reference count drops to zero.
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<P>
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For number rings, another strategy is implemented: There is a cache of,
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for example, the modular integer rings. A modular integer ring is destroyed
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only if its reference count dropped to zero and the cache is about to be
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resized. The effect of this strategy is that recently used rings remain
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cached, whereas undue memory consumption through cached rings is avoided.
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<P><HR><P>
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Go to the <A HREF="cln_1.html">first</A>, <A HREF="cln_9.html">previous</A>, <A HREF="cln_11.html">next</A>, <A HREF="cln_13.html">last</A> section, <A HREF="cln_toc.html">table of contents</A>.
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