84 lines
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84 lines
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<!Converted with LaTeX2HTML 0.6.5 (Tue Nov 15 1994) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds >
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<TITLE>2.1. Numbers</TITLE>
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<meta name="description" value=" Numbers">
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<meta name="resource-type" value="document">
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<b>Common Lisp the Language, 2nd Edition</b>
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<BR> <HR><A NAME=tex2html1705 HREF="node17.html"><IMG ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME=tex2html1703 HREF="node15.html"><IMG ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME=tex2html1697 HREF="node15.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <A NAME=tex2html1707 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="contents" SRC="icons/contents_motif.gif"></A> <A NAME=tex2html1708 HREF="index.html"><IMG ALIGN=BOTTOM ALT="index" SRC="icons/index_motif.gif"></A> <BR>
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<B> Next:</B> <A NAME=tex2html1706 HREF="node17.html"> Integers</A>
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<B>Up:</B> <A NAME=tex2html1704 HREF="node15.html"> Data Types</A>
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<B> Previous:</B> <A NAME=tex2html1698 HREF="node15.html"> Data Types</A>
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<HR> <P>
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<H1><A NAME=SECTION00610000000000000000>2.1. Numbers</A></H1>
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<P>
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Several kinds of numbers are defined in Common Lisp.
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They are divided into <i>integers</i>; <i>ratios</i>;
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<i>floating-point numbers</i>, with names provided for
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up to four different floating-point representations; and <i>complex numbers</i>.
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<P>
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<img align=bottom alt="change_begin" src="gif/change_begin.gif"><br>
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X3J13 voted in March 1989 (REAL-NUMBER-TYPE) <A NAME=493> </A> to add the type <tt>real</tt>.
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<P>
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The <tt>number</tt> data type encompasses all kinds of
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numbers. For convenience, there are names for some
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subclasses of numbers as well. Integers and ratios are of
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type <tt>rational</tt>. Rational numbers and floating-point
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numbers are of type <tt>real</tt>. Real numbers and complex
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numbers are of type <tt>number</tt>.
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<P>
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Although the names of these types were chosen with the
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terminology of mathematics in mind, the correspondences
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are not always exact. Integers and ratios model the
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corresponding mathematical concepts directly. Numbers
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of type <tt>float</tt> may be used to approximate real
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numbers, both rational and irrational. The <tt>real</tt> type
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includes all Common Lisp numbers that represent
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mathematical real numbers, though there are
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mathematical real numbers (irrational numbers)
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that do not have an exact Common Lisp representation.
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Only <tt>real</tt> numbers may be ordered using the <tt><</tt>, <tt>></tt>, <tt><=</tt>,
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and <tt>>=</tt> functions.
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<P>
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<hr>
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<b>Compatibility note:</b>
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The Fortran 77 standard defines the term
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<i>real datum</i> to mean ``a processor approximation to the value
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of a real number.'' In practice the Fortran <i>basic real</i> type
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is the floating-point data type that Common Lisp calls
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<tt>single-float</tt>. The Fortran <i>double precision</i> type is
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Common Lisp's <tt>double-float</tt>. The Pascal <tt>real</tt> data type is
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an ``implementation-defined subset of the real numbers.'' In
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practice this is usually a floating-point type, often what
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Common Lisp calls <tt>double-float</tt>.
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<P>
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A translation of an algorithm written in Fortran or Pascal
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that uses <tt>real</tt> data usually will use some appropriate
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precision of Common Lisp's <tt>float</tt> type. Some algorithms may
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gain accuracy or flexibility by using Common Lisp's
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<tt>rational</tt> or <tt>real</tt> type instead.
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<hr>
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<br><img align=bottom alt="change_end" src="gif/change_end.gif">
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<P>
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<HR>
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<UL>
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<LI> <A NAME=tex2html1709 HREF="node17.html#SECTION00611000000000000000"> Integers</A>
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<LI> <A NAME=tex2html1710 HREF="node18.html#SECTION00612000000000000000"> Ratios</A>
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<LI> <A NAME=tex2html1711 HREF="node19.html#SECTION00613000000000000000"> Floating-Point Numbers</A>
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<LI> <A NAME=tex2html1712 HREF="node20.html#SECTION00614000000000000000"> Complex Numbers</A>
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</UL>
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<BR> <HR><A NAME=tex2html1705 HREF="node17.html"><IMG ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME=tex2html1703 HREF="node15.html"><IMG ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME=tex2html1697 HREF="node15.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <A NAME=tex2html1707 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="contents" SRC="icons/contents_motif.gif"></A> <A NAME=tex2html1708 HREF="index.html"><IMG ALIGN=BOTTOM ALT="index" SRC="icons/index_motif.gif"></A> <BR>
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<B> Next:</B> <A NAME=tex2html1706 HREF="node17.html"> Integers</A>
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<B>Up:</B> <A NAME=tex2html1704 HREF="node15.html"> Data Types</A>
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<B> Previous:</B> <A NAME=tex2html1698 HREF="node15.html"> Data Types</A>
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<HR> <P>
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<HR>
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<P><ADDRESS>
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AI.Repository@cs.cmu.edu
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