64 lines
5.2 KiB
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64 lines
5.2 KiB
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<!-- Common Lisp HyperSpec (TM), version 7.0 generated by Kent M. Pitman on Mon, 11-Apr-2005 2:31am EDT -->
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<TITLE>CLHS: Function PHASE</TITLE>
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<A NAME="phase"><I>Function</I> <B>PHASE</B></A> <P>
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<P><B>Syntax:</B><P>
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<P>
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<B>phase</B> <I>number</I> => <I>phase</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>phase</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="#phase"><B>phase</B></A> returns the phase of <I>number</I> (the angle part of its polar representation) in radians, in the range -<PI> (exclusive) if minus zero is not supported, or -<PI> (inclusive) if minus zero is supported, to <PI> (inclusive). The phase of a positive <A REL=DEFINITION HREF="t_real.htm#real"><I>real</I></A> number is zero; that of a negative <A REL=DEFINITION HREF="t_real.htm#real"><I>real</I></A> number is <PI>. The phase of zero is defined to be zero. <P>
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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_f.htm#float"><I>float</I></A> of the same <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A> as the components of <I>number</I>. 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> of the same <A REL=DEFINITION HREF="26_glo_t.htm#type"><I>type</I></A>. If <I>number</I> is a <A REL=DEFINITION HREF="26_glo_r.htm#rational"><I>rational</I></A> or 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_s.htm#single_float"><I>single float</I></A>. <P>
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The branch cut for <A REL=DEFINITION HREF="#phase"><B>phase</B></A> lies along the negative real axis, continuous with quadrant II. The range consists of that portion of the real axis between -<PI> (exclusive) and <PI> (inclusive). <P>
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The mathematical definition of <A REL=DEFINITION HREF="#phase"><B>phase</B></A> is as follows: <P>
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<TT>(phase </TT><I>x</I><TT>) = (atan (imagpart </TT><I>x</I><TT>) (realpart </TT><I>x</I><TT>))</TT> <P>
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<P><B>Examples:</B><P>
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<P>
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<PRE>
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(phase 1) => 0.0s0
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(phase 0) => 0.0s0
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(phase (cis 30)) => -1.4159266
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(phase #c(0 1)) => 1.5707964
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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><P>
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<P>
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Should signal <A REL=DEFINITION HREF="e_tp_err.htm#type-error"><B>type-error</B></A> if its argument is not a <A REL=DEFINITION HREF="26_glo_n.htm#number"><I>number</I></A>. Might signal <A REL=DEFINITION HREF="e_arithm.htm#arithmetic-error"><B>arithmetic-error</B></A>. <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> None.
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<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/iss290.htm">REAL-NUMBER-TYPE:X3J13-MAR-89</A><LI> <A REL=CHILD HREF="../Issues/iss192.htm">IEEE-ATAN-BRANCH-CUT:SPLIT</A><P></UL><HR>
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