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148 lines
7.7 KiB
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<!DOCTYPE HTML PUBLIC "-//W3O//DTD W3 HTML 2.0//EN">
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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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<HEAD>
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<TITLE>12.3. Comparisons on Numbers</TITLE>
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<BODY>
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<meta name="description" value=" Comparisons on Numbers">
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<meta name="keywords" value="clm">
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<meta name="resource-type" value="document">
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<meta name="distribution" value="global">
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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=tex2html3078 HREF="node125.html"><IMG ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME=tex2html3076 HREF="node121.html"><IMG ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME=tex2html3070 HREF="node123.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <A NAME=tex2html3080 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="contents" SRC="icons/contents_motif.gif"></A> <A NAME=tex2html3081 HREF="index.html"><IMG ALIGN=BOTTOM ALT="index" SRC="icons/index_motif.gif"></A> <BR>
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<B> Next:</B> <A NAME=tex2html3079 HREF="node125.html"> Arithmetic Operations</A>
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<B>Up:</B> <A NAME=tex2html3077 HREF="node121.html"> Numbers</A>
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<B> Previous:</B> <A NAME=tex2html3071 HREF="node123.html"> Predicates on Numbers</A>
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<HR> <P>
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<H1><A NAME=SECTION001630000000000000000>12.3. Comparisons on Numbers</A></H1>
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<P>
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Each of the functions in this section requires that its arguments all be
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numbers; to call one with a non-number is an error. Unless otherwise
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specified, each works on all types of numbers, automatically performing
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any required coercions when arguments are of different types.
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<P>
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<BR><b>[Function]</b><BR>
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<tt>= <i>number</i> &rest <i>more-numbers</i> <BR>
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</tt><tt>/= <i>number</i> &rest <i>more-numbers</i> <BR>
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</tt><tt>< <i>number</i> &rest <i>more-numbers</i> <BR>
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</tt><tt>> <i>number</i> &rest <i>more-numbers</i> <BR>
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</tt><tt><= <i>number</i> &rest <i>more-numbers</i> <BR>
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</tt><tt>>= <i>number</i> &rest <i>more-numbers</i></tt><P>These functions each take one or more arguments. If the sequence
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of arguments satisfies a certain condition:
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<PRE>
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= all the same
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/= all different
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< monotonically increasing
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> monotonically decreasing
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<= monotonically nondecreasing
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>= monotonically nonincreasing
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</PRE>
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then the predicate is true, and otherwise is false.
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Complex numbers may be compared using <tt>=</tt> and <tt>/=</tt>,
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but the others require non-complex arguments.
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Two complex numbers are considered equal by <tt>=</tt>
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if their real parts are equal and their imaginary parts are equal
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according to <tt>=</tt>.
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A complex number may be compared with a non-complex number with <tt>=</tt> or <tt>/=</tt>.
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For example:
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<P><pre>
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(= 3 3) is true. (/= 3 3) is false.
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(= 3 5) is false. (/= 3 5) is true.
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(= 3 3 3 3) is true. (/= 3 3 3 3) is false.
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(= 3 3 5 3) is false. (/= 3 3 5 3) is false.
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(= 3 6 5 2) is false. (/= 3 6 5 2) is true.
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(= 3 2 3) is false. (/= 3 2 3) is false.
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(< 3 5) is true. (<= 3 5) is true.
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(< 3 -5) is false. (<= 3 -5) is false.
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(< 3 3) is false. (<= 3 3) is true.
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(< 0 3 4 6 7) is true. (<= 0 3 4 6 7) is true.
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(< 0 3 4 4 6) is false. (<= 0 3 4 4 6) is true.
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(> 4 3) is true. (>= 4 3) is true.
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(> 4 3 2 1 0) is true. (>= 4 3 2 1 0) is true.
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(> 4 3 3 2 0) is false. (>= 4 3 3 2 0) is true.
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(> 4 3 1 2 0) is false. (>= 4 3 1 2 0) is false.
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(= 3) is true. (/= 3) is true.
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(< 3) is true. (<= 3) is true.
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(= 3.0 #C(3.0 0.0)) is true. (/= 3.0 #C(3.0 1.0)) is true.
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(= 3 3.0) is true. (= 3.0s0 3.0d0) is true.
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(= 0.0 -0.0) is true. (= 5/2 2.5) is true.
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(> 0.0 -0.0) is false. (= 0 -0.0) is true.
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</pre><P>
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With two arguments, these functions perform the usual arithmetic
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comparison tests.
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With three or more arguments, they are useful for range checks,
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as shown in the following example:
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<P><pre>
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(<= 0 x 9) ;true if <tt>x</tt> is between 0 and 9, inclusive
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(< 0.0 x 1.0) ;true if <tt>x</tt> is between 0.0 and 1.0, exclusive
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(< -1 j (length s)) ;true if <tt>j</tt> is a valid index for <tt>s</tt>
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(<= 0 j k (- (length s) 1)) ;true if <tt>j</tt> and <tt>k</tt> are each valid
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; indices for <tt>s</tt> and <b><tt>j</tt><tt>k</tt></b>
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</pre><P>
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<P>
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<hr>
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<b>Rationale:</b> The ``unequality'' relation is called <tt>/=</tt> rather than
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<tt><></tt>
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(the name used in Pascal) for two reasons. First, <tt>/=</tt> of more than two
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arguments is not the same as the <tt>or</tt> of <tt><</tt> and <tt>></tt> of those same
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arguments. Second, unequality is meaningful for complex numbers even though
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<tt><</tt> and <tt>></tt> are not. For both reasons it would be misleading to
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associate unequality with the names of <tt><</tt> and <tt>></tt>.
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<hr>
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<b>Compatibility note:</b> In Common Lisp, the comparison operations
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perform ``mixed-mode'' comparisons: <tt>(= 3 3.0)</tt> is true. In MacLisp,
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there must be exactly two arguments, and they must be either both fixnums
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or both floating-point numbers. To compare two numbers for numerical
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equality and type equality, use <tt>eql</tt>.
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<hr>
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<P>
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<BR><b>[Function]</b><BR>
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<tt>max <i>number</i> &rest <i>more-numbers</i> <BR></tt><tt>min <i>number</i> &rest <i>more-numbers</i></tt><P>The arguments may be any non-complex numbers.
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<tt>max</tt> returns the argument that is greatest (closest
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to positive infinity).
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<tt>min</tt> returns the argument that is least (closest to
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negative infinity).
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<P>
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For <tt>max</tt>,
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if the arguments are a mixture of rationals and floating-point
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numbers, and the largest argument
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is a rational, then the implementation is free to
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produce either that rational or its floating-point approximation;
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if the largest argument is a floating-point number of a smaller format
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than the largest format of any floating-point argument,
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then the implementation is free to
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return the argument in its given format or expanded to the larger format.
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More concisely, the implementation has the choice of returning the largest
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argument as is or applying the rules of floating-point contagion,
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taking all the arguments into consideration for contagion purposes.
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Also, if two or more of the arguments are equal, then any one
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of them may be chosen as the value to return.
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Similar remarks apply to <tt>min</tt> (replacing ``largest argument'' by
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``smallest argument'').
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<P>
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<P><pre>
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(max 6 12) => 12 (min 6 12) => 6
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(max -6 -12) => -6 (min -6 -12) => -12
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(max 1 3 2 -7) => 3 (min 1 3 2 -7) => -7
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(max -2 3 0 7) => 7 (min -2 3 0 7) => -2
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(max 3) => 3 (min 3) => 3
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(max 5.0 2) => 5.0 (min 5.0 2) => 2 <i>or</i> 2.0
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(max 3.0 7 1) => 7 <i>or</i> 7.0 (min 3.0 7 1) => 1 <i>or</i> 1.0
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(max 1.0s0 7.0d0) => 7.0d0
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(min 1.0s0 7.0d0) => 1.0s0 <i>or</i> 1.0d0
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(max 3 1 1.0s0 1.0d0) => 3 <i>or</i> 3.0d0
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(min 3 1 1.0s0 1.0d0) => 1 <i>or</i> 1.0s0 <i>or</i> 1.0d0
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</pre><P>
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<P>
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<BR> <HR><A NAME=tex2html3078 HREF="node125.html"><IMG ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME=tex2html3076 HREF="node121.html"><IMG ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME=tex2html3070 HREF="node123.html"><IMG ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <A NAME=tex2html3080 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="contents" SRC="icons/contents_motif.gif"></A> <A NAME=tex2html3081 HREF="index.html"><IMG ALIGN=BOTTOM ALT="index" SRC="icons/index_motif.gif"></A> <BR>
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<B> Next:</B> <A NAME=tex2html3079 HREF="node125.html"> Arithmetic Operations</A>
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<B>Up:</B> <A NAME=tex2html3077 HREF="node121.html"> Numbers</A>
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<B> Previous:</B> <A NAME=tex2html3071 HREF="node123.html"> Predicates on Numbers</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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</ADDRESS>
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</BODY>
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