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>12. 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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<P>
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<b>Common Lisp the Language, 2nd Edition</b>
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<BR> <HR><A NAME=tex2html3029 HREF="node122.html"><IMG ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME=tex2html3027 HREF="clm.html"><IMG ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME=tex2html3021 HREF="node120.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <A NAME=tex2html3031 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="contents" SRC="icons/contents_motif.gif"></A> <A NAME=tex2html3032 HREF="index.html"><IMG ALIGN=BOTTOM ALT="index" SRC="icons/index_motif.gif"></A> <BR>
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<B> Next:</B> <A NAME=tex2html3030 HREF="node122.html"> PrecisionContagion, and </A>
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<B>Up:</B> <A NAME=tex2html3028 HREF="clm.html">Common Lisp the Language</A>
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<B> Previous:</B> <A NAME=tex2html3022 HREF="node120.html"> An Example</A>
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<HR> <P>
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<H1><A NAME=SECTION001600000000000000000>12. Numbers</A></H1>
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<P>
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<A NAME=NUMBER>Common</A>
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Lisp provides several different representations for numbers.
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These representations may be divided into four categories: integers,
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ratios, floating-point numbers, and complex numbers. Many numeric
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functions will accept any kind of number; they are <i>generic</i>. Other
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functions accept only certain kinds of numbers.
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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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Note that this remark, predating the design of the Common Lisp Object System,
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uses the term ``generic'' in a generic sense and not necessarily
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in the technical sense used by CLOS
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(see chapter <A HREF="node15.html#DTYPES">2</A>).
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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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In general, numbers in Common Lisp are not true objects; <tt>eq</tt> cannot
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be counted upon to operate on them reliably. In particular,
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it is possible that the expression
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<P><pre>
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(let ((x z) (y z)) (eq x y))
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</pre><P>
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may be false rather than true if the value of <tt>z</tt> is a number.
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<P>
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<hr>
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<b>Rationale:</b> This odd breakdown of <tt>eq</tt> in the case of numbers
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allows the implementor enough design freedom to produce exceptionally
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efficient numerical code on conventional architectures.
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MacLisp requires this freedom, for example, in order to produce compiled
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numerical code equal in speed to Fortran.
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Common Lisp makes this same restriction,
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if not for this freedom, then at least for the sake of compatibility.
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<hr>
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<P>
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If two objects are to be compared for ``identity,'' but either might be
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a number, then the predicate <tt>eql</tt> is probably appropriate;
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if both objects are known to be numbers, then <tt>=</tt>
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may be preferable.
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<P>
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<HR>
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<UL>
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<LI> <A NAME=tex2html3033 HREF="node122.html#SECTION001610000000000000000"> Precision, Contagion, and Coercion</A>
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<LI> <A NAME=tex2html3034 HREF="node123.html#SECTION001620000000000000000"> Predicates on Numbers</A>
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<LI> <A NAME=tex2html3035 HREF="node124.html#SECTION001630000000000000000"> Comparisons on Numbers</A>
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<LI> <A NAME=tex2html3036 HREF="node125.html#SECTION001640000000000000000"> Arithmetic Operations</A>
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<LI> <A NAME=tex2html3037 HREF="node126.html#SECTION001650000000000000000"> Irrational and Transcendental Functions</A>
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<UL>
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<LI> <A NAME=tex2html3038 HREF="node127.html#SECTION001651000000000000000"> Exponential and Logarithmic Functions</A>
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<LI> <A NAME=tex2html3039 HREF="node128.html#SECTION001652000000000000000"> Trigonometric and Related Functions</A>
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<LI> <A NAME=tex2html3040 HREF="node129.html#SECTION001653000000000000000"> Branch Cuts, Principal Values, and Boundary Conditions in the Complex Plane</A>
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</UL>
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<LI> <A NAME=tex2html3041 HREF="node130.html#SECTION001660000000000000000"> Type Conversions and Component Extractions on Numbers</A>
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<LI> <A NAME=tex2html3042 HREF="node131.html#SECTION001670000000000000000"> Logical Operations on Numbers</A>
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<LI> <A NAME=tex2html3043 HREF="node132.html#SECTION001680000000000000000"> Byte Manipulation Functions</A>
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<LI> <A NAME=tex2html3044 HREF="node133.html#SECTION001690000000000000000"> Random Numbers</A>
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<LI> <A NAME=tex2html3045 HREF="node134.html#SECTION0016100000000000000000"> Implementation Parameters</A>
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</UL>
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<BR> <HR><A NAME=tex2html3029 HREF="node122.html"><IMG ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME=tex2html3027 HREF="clm.html"><IMG ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME=tex2html3021 HREF="node120.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <A NAME=tex2html3031 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="contents" SRC="icons/contents_motif.gif"></A> <A NAME=tex2html3032 HREF="index.html"><IMG ALIGN=BOTTOM ALT="index" SRC="icons/index_motif.gif"></A> <BR>
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<B> Next:</B> <A NAME=tex2html3030 HREF="node122.html"> PrecisionContagion, and </A>
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<B>Up:</B> <A NAME=tex2html3028 HREF="clm.html">Common Lisp the Language</A>
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<B> Previous:</B> <A NAME=tex2html3022 HREF="node120.html"> An Example</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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