80 lines
7.8 KiB
HTML
80 lines
7.8 KiB
HTML
<!-- Common Lisp HyperSpec (TM), version 7.0 generated by Kent M. Pitman on Mon, 11-Apr-2005 2:31am EDT -->
|
|
<HTML>
|
|
<HEAD>
|
|
<TITLE>CLHS: Section 12.1.1</TITLE>
|
|
<LINK HREF="../Data/clhs.css" REL="stylesheet" TYPE="text/css" />
|
|
<META HTTP-EQUIV="Author" CONTENT="Kent M. Pitman">
|
|
<META HTTP-EQUIV="Organization" CONTENT="LispWorks Ltd.">
|
|
<LINK REL=TOP HREF="../Front/index.htm">
|
|
<LINK REL=COPYRIGHT HREF="../Front/Help.htm#Legal">
|
|
<LINK REL=DISCLAIMER HREF="../Front/Help.htm#Disclaimer">
|
|
<LINK REL=PREV HREF="12_a.htm">
|
|
<LINK REL=UP HREF="12_a.htm">
|
|
<LINK REL=NEXT HREF="12_aaa.htm">
|
|
</HEAD>
|
|
<BODY>
|
|
<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_a.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Previous]" SRC="../Graphics/Prev.gif" ALIGN=Bottom></A><A REL=UP HREF="12_a.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Up]" SRC="../Graphics/Up.gif" ALIGN=Bottom></A><A REL=NEXT HREF="12_aaa.htm"><IMG WIDTH=40 HEIGHT=40 ALT="[Next]" SRC="../Graphics/Next.gif" ALIGN=Bottom></A></H1>
|
|
|
|
<HR>
|
|
|
|
<H2>
|
|
12.1.1 Numeric Operations</H2> <P>
|
|
Common Lisp provides a large variety of operations related to <A REL=DEFINITION HREF="26_glo_n.htm#number"><I>numbers</I></A>. This section provides an overview of those operations by grouping them into categories that emphasize some of the relationships among them. <P>
|
|
The next figure shows <A REL=DEFINITION HREF="26_glo_o.htm#operator"><I>operators</I></A> relating to arithmetic operations. <P>
|
|
<PRE>
|
|
<A REL=DEFINITION HREF="a_st.htm#ST">*</A> <A REL=DEFINITION HREF="f_1pl_1_.htm#1PL">1+</A> <A REL=DEFINITION HREF="f_gcd.htm#gcd">gcd</A>
|
|
<A REL=DEFINITION HREF="a_pl.htm#PL">+</A> <A REL=DEFINITION HREF="f_1pl_1_.htm#1-">1-</A> <A REL=DEFINITION HREF="m_incf_.htm#incf">incf</A>
|
|
<A REL=DEFINITION HREF="a__.htm#-">-</A> <A REL=DEFINITION HREF="f_conjug.htm#conjugate">conjugate</A> <A REL=DEFINITION HREF="f_lcm.htm#lcm">lcm</A>
|
|
<A REL=DEFINITION HREF="a_sl.htm#SL">/</A> <A REL=DEFINITION HREF="m_incf_.htm#decf">decf</A>
|
|
</PRE>
|
|
<P><B>Figure 12-1. Operators relating to Arithmetic.</B> <P>
|
|
The next figure shows <A REL=DEFINITION HREF="26_glo_d.htm#defined_name"><I>defined names</I></A> relating to exponential, logarithmic, and trigonometric operations. <P>
|
|
<PRE>
|
|
<A REL=DEFINITION HREF="f_abs.htm#abs">abs</A> <A REL=DEFINITION HREF="f_sin_c.htm#cos">cos</A> <A REL=DEFINITION HREF="f_signum.htm#signum">signum</A>
|
|
<A REL=DEFINITION HREF="f_asin_.htm#acos">acos</A> <A REL=DEFINITION HREF="f_sinh_.htm#cosh">cosh</A> <A REL=DEFINITION HREF="f_sin_c.htm#sin">sin</A>
|
|
<A REL=DEFINITION HREF="f_sinh_.htm#acosh">acosh</A> <A REL=DEFINITION HREF="f_exp_e.htm#exp">exp</A> <A REL=DEFINITION HREF="f_sinh_.htm#sinh">sinh</A>
|
|
<A REL=DEFINITION HREF="f_asin_.htm#asin">asin</A> <A REL=DEFINITION HREF="f_exp_e.htm#expt">expt</A> <A REL=DEFINITION HREF="f_sqrt_.htm#sqrt">sqrt</A>
|
|
<A REL=DEFINITION HREF="f_sinh_.htm#asinh">asinh</A> <A REL=DEFINITION HREF="f_sqrt_.htm#isqrt">isqrt</A> <A REL=DEFINITION HREF="f_sin_c.htm#tan">tan</A>
|
|
<A REL=DEFINITION HREF="f_asin_.htm#atan">atan</A> <A REL=DEFINITION HREF="f_log.htm#log">log</A> <A REL=DEFINITION HREF="f_sinh_.htm#tanh">tanh</A>
|
|
<A REL=DEFINITION HREF="f_sinh_.htm#atanh">atanh</A> <A REL=DEFINITION HREF="f_phase.htm#phase">phase</A>
|
|
<A REL=DEFINITION HREF="f_cis.htm#cis">cis</A> <A REL=DEFINITION HREF="v_pi.htm#pi">pi</A>
|
|
</PRE>
|
|
<P><B>Figure 12-2. Defined names relating to Exponentials, Logarithms, and Trigonometry.</B> <P>
|
|
The next figure shows <A REL=DEFINITION HREF="26_glo_o.htm#operator"><I>operators</I></A> relating to numeric comparison and predication. <P>
|
|
<PRE>
|
|
<A REL=DEFINITION HREF="f_eq_sle.htm#SLEQ">/=</A> <A REL=DEFINITION HREF="f_eq_sle.htm#GTEQ">>=</A> <A REL=DEFINITION HREF="f_evenpc.htm#oddp">oddp</A>
|
|
<A REL=DEFINITION HREF="f_eq_sle.htm#LT"><</A> <A REL=DEFINITION HREF="f_evenpc.htm#evenp">evenp</A> <A REL=DEFINITION HREF="f_minusp.htm#plusp">plusp</A>
|
|
<A REL=DEFINITION HREF="f_eq_sle.htm#LTEQ"><=</A> <A REL=DEFINITION HREF="f_max_m.htm#max">max</A> <A REL=DEFINITION HREF="f_zerop.htm#zerop">zerop</A>
|
|
<A REL=DEFINITION HREF="f_eq_sle.htm#EQ">=</A> <A REL=DEFINITION HREF="f_max_m.htm#min">min</A>
|
|
<A REL=DEFINITION HREF="f_eq_sle.htm#GT">></A> <A REL=DEFINITION HREF="f_minusp.htm#minusp">minusp</A>
|
|
</PRE>
|
|
<P><B>Figure 12-3. Operators for numeric comparison and predication.</B> <P>
|
|
The next figure shows <A REL=DEFINITION HREF="26_glo_d.htm#defined_name"><I>defined names</I></A> relating to numeric type manipulation and coercion. <P>
|
|
<PRE>
|
|
<A REL=DEFINITION HREF="f_floorc.htm#ceiling">ceiling</A> <A REL=DEFINITION HREF="f_dec_fl.htm#float-radix">float-radix</A> <A REL=DEFINITION HREF="a_ration.htm#rational">rational</A>
|
|
<A REL=DEFINITION HREF="a_comple.htm#complex">complex</A> <A REL=DEFINITION HREF="f_dec_fl.htm#float-sign">float-sign</A> <A REL=DEFINITION HREF="f_ration.htm#rationalize">rationalize</A>
|
|
<A REL=DEFINITION HREF="f_dec_fl.htm#decode-float">decode-float</A> <A REL=DEFINITION HREF="f_floorc.htm#floor">floor</A> <A REL=DEFINITION HREF="f_realpa.htm#realpart">realpart</A>
|
|
<A REL=DEFINITION HREF="f_numera.htm#denominator">denominator</A> <A REL=DEFINITION HREF="f_floorc.htm#fround">fround</A> <A REL=DEFINITION HREF="f_mod_r.htm#rem">rem</A>
|
|
<A REL=DEFINITION HREF="f_floorc.htm#fceiling">fceiling</A> <A REL=DEFINITION HREF="f_floorc.htm#ftruncate">ftruncate</A> <A REL=DEFINITION HREF="f_floorc.htm#round">round</A>
|
|
<A REL=DEFINITION HREF="f_floorc.htm#ffloor">ffloor</A> <A REL=DEFINITION HREF="f_realpa.htm#imagpart">imagpart</A> <A REL=DEFINITION HREF="f_dec_fl.htm#scale-float">scale-float</A>
|
|
<A REL=DEFINITION HREF="a_float.htm#float">float</A> <A REL=DEFINITION HREF="f_dec_fl.htm#integer-decode-float">integer-decode-float</A> <A REL=DEFINITION HREF="f_floorc.htm#truncate">truncate</A>
|
|
<A REL=DEFINITION HREF="f_dec_fl.htm#float-digits">float-digits</A> <A REL=DEFINITION HREF="a_mod.htm#mod">mod</A>
|
|
<A REL=DEFINITION HREF="f_dec_fl.htm#float-precision">float-precision</A> <A REL=DEFINITION HREF="f_numera.htm#numerator">numerator</A>
|
|
</PRE>
|
|
<P><B>Figure 12-4. Defined names relating to numeric type manipulation and coercion.</B> <P>
|
|
|
|
|
|
<A REL=CHILD HREF="12_aaa.htm"><H2>
|
|
12.1.1.1 Associativity and Commutativity in Numeric Operations</H2></A><P>
|
|
|
|
<A REL=CHILD HREF="12_aab.htm"><H2>
|
|
12.1.1.2 Contagion in Numeric Operations</H2></A><P>
|
|
|
|
<A REL=CHILD HREF="12_aac.htm"><H2>
|
|
12.1.1.3 Viewing Integers as Bits and Bytes</H2></A><P><HR>
|
|
|
|
<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>
|
|
|
|
<A REL=COPYRIGHT HREF="../Front/Help.htm#Legal"><I>Copyright 1996-2005, LispWorks Ltd. All rights reserved.</I></A><P>
|
|
</BODY>
|
|
</HTML>
|