66 lines
4.7 KiB
HTML
66 lines
4.7 KiB
HTML
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<TITLE>CLHS: Function ABS</TITLE>
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<A NAME="abs"><I>Function</I> <B>ABS</B></A> <P>
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<P><B>Syntax:</B><P>
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<P>
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<B>abs</B> <I>number</I> => <I>absolute-value</I><P>
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<P>
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<P><B>Arguments and Values:</B><P>
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<P>
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<I>number</I>---a <A REL=DEFINITION HREF="26_glo_n.htm#number"><I>number</I></A>. <P>
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<I>absolute-value</I>---a non-negative <A REL=DEFINITION HREF="t_real.htm#real"><I>real</I></A>. <P>
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<P><B>Description:</B><P>
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<P>
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<A REL=DEFINITION HREF="#abs"><B>abs</B></A> returns the absolute value of <I>number</I>. <P>
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If <I>number</I> is a <A REL=DEFINITION HREF="t_real.htm#real"><I>real</I></A>, the result is of the same <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A> as <I>number</I>. <P>
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If <I>number</I> is a <A REL=DEFINITION HREF="26_glo_c.htm#complex"><I>complex</I></A>, the result is a positive <A REL=DEFINITION HREF="t_real.htm#real"><I>real</I></A> with the same magnitude as <I>number</I>. The result can be a <A REL=DEFINITION HREF="26_glo_f.htm#float"><I>float</I></A> even if <I>number</I>'s components are <A REL=DEFINITION HREF="26_glo_r.htm#rational"><I>rationals</I></A> and an exact rational result would have been possible. Thus the result of <TT>(abs #c(3 4))</TT> can be either <TT>5</TT> or <TT>5.0</TT>, depending on the implementation. <P>
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<P><B>Examples:</B><P>
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<P>
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<PRE>
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(abs 0) => 0
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(abs 12/13) => 12/13
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(abs -1.09) => 1.09
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(abs #c(5.0 -5.0)) => 7.071068
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(abs #c(5 5)) => 7.071068
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(abs #c(3/5 4/5)) => 1 or approximately 1.0
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(eql (abs -0.0) -0.0) => <A REL=DEFINITION HREF="26_glo_t.htm#true">true</A>
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</PRE>
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</TT> <P>
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<P><B>Affected By:</B> None.
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<P>
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<P><B>Exceptional Situations:</B> None.
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<P>
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<P><B>See Also:</B><P>
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<P>
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<A REL=CHILD HREF="12_acc.htm">Section 12.1.3.3 (Rule of Float Substitutability)</A> <P>
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<P><B>Notes:</B><P>
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<P>
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If <I>number</I> is a <A REL=DEFINITION HREF="26_glo_c.htm#complex"><I>complex</I></A>, the result is equivalent to the following: <P>
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<TT>(sqrt (+ (expt (realpart </TT><I>number</I><TT>) 2) (expt (imagpart </TT><I>number</I><TT>) 2)))</TT> <P>
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An implementation should not use this formula directly for all <A REL=DEFINITION HREF="26_glo_c.htm#complex"><I>complexes</I></A> but should handle very large or very small components specially to avoid intermediate overflow or underflow. <P>
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<P><HR>The following <A REL=META HREF="../Front/X3J13Iss.htm">X3J13 cleanup issues</A>, <I>not part of the specification</I>, apply to this section:<P><UL><LI> <A REL=CHILD HREF="../Issues/iss071.htm">COMPLEX-RATIONAL-RESULT:EXTEND</A><LI> <A REL=CHILD HREF="../Issues/iss290.htm">REAL-NUMBER-TYPE:X3J13-MAR-89</A><P></UL><HR>
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