71 lines
5.4 KiB
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71 lines
5.4 KiB
HTML
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<TITLE>CLHS: Function SIGNUM</TITLE>
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<A NAME="signum"><I>Function</I> <B>SIGNUM</B></A> <P>
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<P><B>Syntax:</B><P>
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<P>
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<B>signum</B> <I>number</I> => <I>signed-prototype</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>signed-prototype</I>---a <A REL=DEFINITION HREF="26_glo_n.htm#number"><I>number</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="#signum"><B>signum</B></A> determines a numerical value that indicates whether <I>number</I> is negative, zero, or positive. <P>
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For a <A REL=DEFINITION HREF="26_glo_r.htm#rational"><I>rational</I></A>, <A REL=DEFINITION HREF="#signum"><B>signum</B></A> returns one of <TT>-1</TT>, <TT>0</TT>, or <TT>1</TT> according to whether <I>number</I> is negative, zero, or positive. For a <A REL=DEFINITION HREF="26_glo_f.htm#float"><I>float</I></A>, the result is a <A REL=DEFINITION HREF="26_glo_f.htm#float"><I>float</I></A> of the same format whose value is minus one, zero, or one. For a <A REL=DEFINITION HREF="26_glo_c.htm#complex"><I>complex</I></A> number <TT>z</TT>, <TT>(signum </TT><I>z</I><TT>)</TT> is a complex number of the same phase but with unit magnitude, unless <TT>z</TT> is a complex zero, in which case the result is <TT>z</TT>. <P>
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For <A REL=DEFINITION HREF="26_glo_r.htm#rational"><I>rational</I></A> <A REL=DEFINITION HREF="26_glo_a.htm#argument"><I>arguments</I></A>, <A REL=DEFINITION HREF="#signum"><B>signum</B></A> is a rational function, but it may be irrational for <A REL=DEFINITION HREF="26_glo_c.htm#complex"><I>complex</I></A> <A REL=DEFINITION HREF="26_glo_a.htm#argument"><I>arguments</I></A>. <P>
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If <I>number</I> is a <A REL=DEFINITION HREF="26_glo_f.htm#float"><I>float</I></A>, the result is a <A REL=DEFINITION HREF="26_glo_f.htm#float"><I>float</I></A>. If <I>number</I> is a <A REL=DEFINITION HREF="26_glo_r.htm#rational"><I>rational</I></A>, the result is a <A REL=DEFINITION HREF="26_glo_r.htm#rational"><I>rational</I></A>. If <I>number</I> is a <A REL=DEFINITION HREF="26_glo_c.htm#complex_float"><I>complex float</I></A>, the result is a <A REL=DEFINITION HREF="26_glo_c.htm#complex_float"><I>complex float</I></A>. If <I>number</I> is a <A REL=DEFINITION HREF="26_glo_c.htm#complex_rational"><I>complex rational</I></A>, the result is a <A REL=DEFINITION HREF="26_glo_c.htm#complex"><I>complex</I></A>, but it is <A REL=DEFINITION HREF="26_glo_i.htm#implementation-dependent"><I>implementation-dependent</I></A> whether that result is a <A REL=DEFINITION HREF="26_glo_c.htm#complex_rational"><I>complex rational</I></A> or a <A REL=DEFINITION HREF="26_glo_c.htm#complex_float"><I>complex float</I></A>. <P>
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<P><B>Examples:</B><P>
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<P>
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<PRE>
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(signum 0) => 0
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(signum 99) => 1
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(signum 4/5) => 1
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(signum -99/100) => -1
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(signum 0.0) => 0.0
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(signum #c(0 33)) => #C(0.0 1.0)
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(signum #c(7.5 10.0)) => #C(0.6 0.8)
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(signum #c(0.0 -14.7)) => #C(0.0 -1.0)
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(eql (signum -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>Side Effects:</B> None.
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<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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<PRE>
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(signum x) == (if (zerop x) x (/ x (abs x)))
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</PRE>
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