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33 lines
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<TITLE>CLHS: Section 12.1.1.1</TITLE>
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<H1><A REV=MADE HREF="http://www.lispworks.com/"><IMG WIDTH=80 HEIGHT=65 ALT="[LISPWORKS]" SRC="../Graphics/LWSmall.gif" ALIGN=Bottom></A><A REL=TOP HREF="../Front/index.htm"><IMG WIDTH=237 HEIGHT=65 ALT="[Common Lisp HyperSpec (TM)]" SRC="../Graphics/CLHS_Sm.gif" ALIGN=Bottom></A> <A REL=PREV HREF="12_aa.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Previous]" SRC="../Graphics/Prev.gif" ALIGN=Bottom></A><A REL=UP HREF="12_aa.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Up]" SRC="../Graphics/Up.gif" ALIGN=Bottom></A><A REL=NEXT HREF="12_aaaa.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Next]" SRC="../Graphics/Next.gif" ALIGN=Bottom></A></H1>
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<H2>
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12.1.1.1 Associativity and Commutativity in Numeric Operations</H2> <P>
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For functions that are mathematically associative (and possibly commutative), a <A REL=DEFINITION HREF="26_glo_c.htm#conforming_implementation"><I>conforming implementation</I></A> may process the <A REL=DEFINITION HREF="26_glo_a.htm#argument"><I>arguments</I></A> in any manner consistent with associative (and possibly commutative) rearrangement. This does not affect the order in which the <A REL=DEFINITION HREF="26_glo_a.htm#argument"><I>argument</I></A> <A REL=DEFINITION HREF="26_glo_f.htm#form"><I>forms</I></A> are <I>evaluated</I>; for a discussion of evaluation order, see <A REL=CHILD HREF="03_ababc.htm">Section 3.1.2.1.2.3 (Function Forms)</A>. What is unspecified is only the order in which the <A REL=DEFINITION HREF="26_glo_p.htm#parameter"><I>parameter</I></A> <A REL=DEFINITION HREF="26_glo_v.htm#value"><I>values</I></A> are processed. This implies that <A REL=DEFINITION HREF="26_glo_i.htm#implementation"><I>implementations</I></A> may differ in which automatic <I>coercions</I> are applied; see <A REL=CHILD HREF="12_aab.htm">Section 12.1.1.2 (Contagion in Numeric Operations)</A>. <P>
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A <A REL=DEFINITION HREF="26_glo_c.htm#conforming_program"><I>conforming program</I></A> can control the order of processing explicitly by separating the operations into separate (possibly nested) <A REL=DEFINITION HREF="26_glo_f.htm#function_form"><I>function forms</I></A>, or by writing explicit calls to <A REL=DEFINITION HREF="26_glo_f.htm#function"><I>functions</I></A> that perform coercions. <P>
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<A REL=CHILD HREF="12_aaaa.htm"><H2>
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12.1.1.1.1 Examples of Associativity and Commutativity in Numeric Operations</H2></A><P><HR>
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<A REL=NAVIGATOR HREF="../Front/StartPts.htm"><IMG WIDTH=80 HEIGHT=40 ALT="[Starting Points]" SRC="../Graphics/StartPts.gif" ALIGN=Bottom></A><A REL=TOC HREF="../Front/Contents.htm"><IMG WIDTH=80 HEIGHT=40 ALT="[Contents]" SRC="../Graphics/Contents.gif" ALIGN=Bottom></A><A REL=INDEX HREF="../Front/X_Master.htm"><IMG WIDTH=80 HEIGHT=40 ALT="[Index]" SRC="../Graphics/Index.gif" ALIGN=Bottom></A><A REL=INDEX HREF="../Front/X_Symbol.htm"><IMG WIDTH=80 HEIGHT=40 ALT="[Symbols]" SRC="../Graphics/Symbols.gif" ALIGN=Bottom></A><A REL=GLOSSARY HREF="../Body/26_a.htm"><IMG WIDTH=80 HEIGHT=40 ALT="[Glossary]" SRC="../Graphics/Glossary.gif" ALIGN=Bottom></A><A HREF="../Front/X3J13Iss.htm"><IMG WIDTH=80 HEIGHT=40 ALT="[Issues]" SRC="../Graphics/Issues.gif" ALIGN=Bottom></A><BR>
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<A REL=COPYRIGHT HREF="../Front/Help.htm#Legal"><I>Copyright 1996-2005, LispWorks Ltd. All rights reserved.</I></A><P>
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