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<!DOCTYPE HTML>
<HTML LANG="en-us"
><HEAD
><TITLE
>abs | Common Lisp Nova Spec</TITLE
><META CHARSET="US-ASCII"
><LINK REL="canonical" HREF="f_abs.html"
><LINK REL="next" HREF="f_evenp.html" TYPE="text/html" TITLE="evenp, oddp"
><LINK REL="prev" HREF="f_1_plus.html" TYPE="text/html" TITLE="1+, 1&#8722;"
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></SCRIPT
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></SCRIPT
></HEAD
><BODY
><DIV
><DIV CLASS="topnav"
><DIV CLASS="breadcrumb"
><SPAN CLASS="breadcrumb-item"
><A HREF="index.html"
>Common Lisp Nova Spec</A
></SPAN
> <SPAN CLASS="breadcrumb-item"
>&#8594; <A HREF="12_Numbers.html"
>12. Numbers</A
></SPAN
> <SPAN CLASS="breadcrumb-item"
>&#8594; <A HREF="12_2_Numbers_Dictionary.html"
>12.2 Numbers Dictionary</A
></SPAN
> <SPAN CLASS="breadcrumb-item"
>&#8594; <A HREF="f_abs.html"
>abs</A
></SPAN
></DIV
><DIV CLASS="apropos"
><DIV CLASS="apropos-io"
><A HREF="f_1_plus.html" CLASS="prev"
>&#8592;</A
><SPAN ID="apropos-label"
>Apropos </SPAN
><INPUT ID="apropos" AUTOFOCUS="AUTOFOCUS" PLACEHOLDER="Type here to search" ONINPUT="aproposInput(this);" ONKEYUP="aproposKeyup(event);" ONCHANGE="aproposChange(this);" ONFOCUS="aproposFocus(this);" ONFOCUSOUT="aproposFocusout(this);"
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><DIV CLASS="matter"
><DIV CLASS="com"
><DIV CLASS="begincom"
><HR
><TABLE WIDTH="100%" CELLSPACING="0" CELLPADDING="0"
><TR
><TD ALIGN="LEFT" VALIGN="BASELINE" WIDTH="100%" CLASS="name"
><SPAN CLASS="idx" DATA-KIND="idxref" DATA-TERM="abs"
></SPAN
><B
>abs</B
></TD
><TD ALIGN="RIGHT" VALIGN="BASELINE" WIDTH="0" NOWRAP="NOWRAP" CLASS="ftype"
><I
>Function</I
></TD
></TR
></TABLE
><HR
></DIV
><UL CLASS="subtoc"
></UL
><DL
><DT
><B
>Syntax</B
></DT
><DD
><P CLASS="j"
><B
>abs</B
> <SPAN CLASS="cmssi"
>number</SPAN
> <SPAN CLASS="arrow"
>&#8594;</SPAN
> <SPAN CLASS="cmssi"
>absolute-value</SPAN
></P
></DD
><DT
><B
>Arguments and Values</B
></DT
><DD
><P CLASS="j"
><VAR CLASS="param"
>number</VAR
> &#8212; a <A HREF="26_1_Glossary.html#number"
><EM CLASS="term"
>number</EM
></A
>. </P
><P CLASS="j"
><VAR CLASS="param"
>absolute-value</VAR
> &#8212; a non-negative <EM CLASS="term"
>real</EM
>.</P
></DD
><DT
><B
>Description</B
></DT
><DD
><P CLASS="j"
><A HREF="f_abs.html" CLASS="funref"
><B
>abs</B
></A
> returns the absolute value of <VAR CLASS="param"
>number</VAR
>. </P
><P CLASS="j"
>If <VAR CLASS="param"
>number</VAR
> is a <EM CLASS="term"
>real</EM
>, the result is of the same <A HREF="26_1_Glossary.html#type"
><EM CLASS="term"
>type</EM
></A
> as <VAR CLASS="param"
>number</VAR
>. </P
><P CLASS="j"
>If <VAR CLASS="param"
>number</VAR
> is a <A HREF="26_1_Glossary.html#complex"
><EM CLASS="term"
>complex</EM
></A
>, the result is a positive <EM CLASS="term"
>real</EM
> with the same magnitude as <VAR CLASS="param"
>number</VAR
>. The result can be a <A HREF="26_1_Glossary.html#float"
><EM CLASS="term"
>float</EM
></A
> even if <VAR CLASS="param"
>number</VAR
>&#8217;s components are <A HREF="26_1_Glossary.html#rational"
><EM CLASS="term"
>rationals</EM
></A
> and an exact rational result would have been possible. Thus the result of <CODE CLASS="f"
>(abs #c(3 4))</CODE
> can be either <CODE CLASS="f"
>5</CODE
> or <CODE CLASS="f"
>5.0</CODE
>, depending on the implementation.</P
></DD
><DT
><B
>Examples</B
></DT
><DD
><PRE CLASS="screen"
>(abs 0) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 0
(abs 12/13) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 12/13
(abs -1.09) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 1.09
(abs #c(5.0 -5.0)) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 7.071068
(abs #c(5 5)) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 7.071068
(abs #c(3/5 4/5)) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> 1 or approximately 1.0
(eql (abs -0.0) -0.0) <SPAN CLASS="cmsy"
><SPAN CLASS="arrow"
>&#8594;</SPAN
></SPAN
> <A HREF="26_1_Glossary.html#true"
><EM CLASS="term"
>true</EM
></A
></PRE
></DD
><DT
><B
>See Also</B
></DT
><DD
><P CLASS="j"
><A HREF="12_1_Number_Concepts.html#sec_12_1_3_3" CLASS="secref"
><SPAN CLASS="cmr"
>Section</SPAN
> <SPAN CLASS="cmr"
>12.1.3.3</SPAN
> <SPAN CLASS="cmr"
>(Rule</SPAN
> <SPAN CLASS="cmr"
>of</SPAN
> <SPAN CLASS="cmr"
>Float</SPAN
> <SPAN CLASS="cmr"
>Substitutability)</SPAN
></A
></P
></DD
><DT
><B
>Notes</B
></DT
><DD
><P CLASS="j"
>If <VAR CLASS="param"
>number</VAR
> is a <A HREF="26_1_Glossary.html#complex"
><EM CLASS="term"
>complex</EM
></A
>, the result is equivalent to the following: </P
><P CLASS="j"
><CODE CLASS="f"
>(sqrt (+ (expt (realpart <VAR CLASS="param"
>number</VAR
>) 2) (expt (imagpart <VAR CLASS="param"
>number</VAR
>) 2)))</CODE
> </P
><P CLASS="j"
>An implementation should not use this formula directly for all <A HREF="26_1_Glossary.html#complex"
><EM CLASS="term"
>complexes</EM
></A
> but should handle very large or very small components specially to avoid intermediate overflow or underflow.</P
></DD
></DL
></DIV
></DIV
><DIV CLASS="footer"
><DIV CLASS="btmnav"
><A HREF="f_1_plus.html" CLASS="prev"
>&#8592;</A
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>&#8594;</A
></DIV
><DIV CLASS="trail"
>Conversion to HTML copyright 2023 by Gilbert Baumann</DIV
></DIV
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>domReady();</SCRIPT
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