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35 lines
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<TITLE>CLHS: Section 12.1.4.1</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_ad.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Previous]" SRC="../Graphics/Prev.gif" ALIGN=Bottom></A><A REL=UP HREF="12_ad.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Up]" SRC="../Graphics/Up.gif" ALIGN=Bottom></A><A REL=NEXT HREF="12_adaa.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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12.1.4.1 Rule of Float and Rational Contagion</H2> <P>
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When <A REL=DEFINITION HREF="26_glo_r.htm#rational"><I>rationals</I></A> and <A REL=DEFINITION HREF="26_glo_f.htm#float"><I>floats</I></A> are combined by a numerical function, the <A REL=DEFINITION HREF="26_glo_r.htm#rational"><I>rational</I></A> is first converted to a <A REL=DEFINITION HREF="26_glo_f.htm#float"><I>float</I></A> of the same format. For <A REL=DEFINITION HREF="26_glo_f.htm#function"><I>functions</I></A> such as <A REL=DEFINITION HREF="f_pl.htm#PL"><B>+</B></A> that take more than two arguments, it is permitted that part of the operation be carried out exactly using <A REL=DEFINITION HREF="26_glo_r.htm#rational"><I>rationals</I></A> and the rest be done using floating-point arithmetic. <P>
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When <A REL=DEFINITION HREF="26_glo_r.htm#rational"><I>rationals</I></A> and <A REL=DEFINITION HREF="26_glo_f.htm#float"><I>floats</I></A> are compared by a numerical function, the <A REL=DEFINITION HREF="26_glo_f.htm#function"><I>function</I></A> <A REL=DEFINITION HREF="f_ration.htm#rational"><B>rational</B></A> is effectively called to convert the <A REL=DEFINITION HREF="26_glo_f.htm#float"><I>float</I></A> to a <A REL=DEFINITION HREF="26_glo_r.htm#rational"><I>rational</I></A> and then an exact comparison is performed. In the case of <A REL=DEFINITION HREF="26_glo_c.htm#complex"><I>complex</I></A> numbers, the real and imaginary parts are effectively handled individually. <P>
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<A REL=CHILD HREF="12_adaa.htm"><H2>
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12.1.4.1.1 Examples of Rule of Float and Rational Contagion</H2></A><P> <P>
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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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