131 lines
5.0 KiB
HTML
131 lines
5.0 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<link type="text/css" rel="stylesheet" href="style.css"><!-- Generated by The Open Group's rhtm tool v1.2.1 -->
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<!-- Copyright (c) 2001 The Open Group, All Rights Reserved -->
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<title>cproj</title>
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<body bgcolor="white">
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<script type="text/javascript" language="JavaScript" src="../jscript/codes.js">
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</script>
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<basefont size="3"> <a name="cproj"></a> <a name="tag_03_91"></a><!-- cproj -->
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<!--header start-->
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<center><font size="2">The Open Group Base Specifications Issue 6<br>
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IEEE Std 1003.1-2001<br>
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Copyright © 2001 The IEEE and The Open Group, All Rights reserved.</font></center>
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<!--header end-->
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<hr size="2" noshade>
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<h4><a name="tag_03_91_01"></a>NAME</h4>
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<blockquote>cproj, cprojf, cprojl - complex projection functions</blockquote>
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<h4><a name="tag_03_91_02"></a>SYNOPSIS</h4>
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<blockquote class="synopsis">
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<p><code><tt>#include <<a href="../basedefs/complex.h.html">complex.h</a>><br>
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<br>
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double complex cproj(double complex</tt> <i>z</i><tt>);<br>
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float complex cprojf(float complex</tt> <i>z</i><tt>);<br>
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long double complex cprojl(long double complex</tt> <i>z</i><tt>);<br>
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</tt></code></p>
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</blockquote>
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<h4><a name="tag_03_91_03"></a>DESCRIPTION</h4>
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<blockquote>
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<div class="box"><sup>[<a href="javascript:open_code('CX')">CX</a>]</sup> <img src="../images/opt-start.gif" alt="[Option Start]"
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border="0"> The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the
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requirements described here and the ISO C standard is unintentional. This volume of IEEE Std 1003.1-2001 defers to
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the ISO C standard. <img src="../images/opt-end.gif" alt="[Option End]" border="0"></div>
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<p>These functions shall compute a projection of <i>z</i> onto the Riemann sphere: <i>z</i> projects to <i>z</i>, except that all
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complex infinities (even those with one infinite part and one NaN part) project to positive infinity on the real axis. If <i>z</i>
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has an infinite part, then <i>cproj</i>( <i>z</i>) shall be equivalent to:</p>
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<pre>
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<tt>INFINITY + I * copysign(0.0, cimag(z))
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</tt>
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</pre>
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</blockquote>
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<h4><a name="tag_03_91_04"></a>RETURN VALUE</h4>
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<blockquote>
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<p>These functions shall return the value of the projection onto the Riemann sphere.</p>
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</blockquote>
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<h4><a name="tag_03_91_05"></a>ERRORS</h4>
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<blockquote>
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<p>No errors are defined.</p>
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</blockquote>
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<hr>
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<div class="box"><em>The following sections are informative.</em></div>
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<h4><a name="tag_03_91_06"></a>EXAMPLES</h4>
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<blockquote>
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<p>None.</p>
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</blockquote>
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<h4><a name="tag_03_91_07"></a>APPLICATION USAGE</h4>
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<blockquote>
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<p>None.</p>
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</blockquote>
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<h4><a name="tag_03_91_08"></a>RATIONALE</h4>
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<blockquote>
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<p>Two topologies are commonly used in complex mathematics: the complex plane with its continuum of infinities, and the Riemann
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sphere with its single infinity. The complex plane is better suited for transcendental functions, the Riemann sphere for algebraic
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functions. The complex types with their multiplicity of infinities provide a useful (though imperfect) model for the complex plane.
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The <i>cproj</i>() function helps model the Riemann sphere by mapping all infinities to one, and should be used just before any
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operation, especially comparisons, that might give spurious results for any of the other infinities. Note that a complex value with
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one infinite part and one NaN part is regarded as an infinity, not a NaN, because if one part is infinite, the complex value is
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infinite independent of the value of the other part. For the same reason, <a href="../functions/cabs.html"><i>cabs</i>()</a>
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returns an infinity if its argument has an infinite part and a NaN part.</p>
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</blockquote>
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<h4><a name="tag_03_91_09"></a>FUTURE DIRECTIONS</h4>
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<blockquote>
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<p>None.</p>
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</blockquote>
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<h4><a name="tag_03_91_10"></a>SEE ALSO</h4>
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<blockquote>
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<p><a href="carg.html"><i>carg</i>()</a> , <a href="cimag.html"><i>cimag</i>()</a> , <a href="conj.html"><i>conj</i>()</a> , <a
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href="creal.html"><i>creal</i>()</a> , the Base Definitions volume of IEEE Std 1003.1-2001, <a href=
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"../basedefs/complex.h.html"><i><complex.h></i></a></p>
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</blockquote>
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<h4><a name="tag_03_91_11"></a>CHANGE HISTORY</h4>
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<blockquote>
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<p>First released in Issue 6. Derived from the ISO/IEC 9899:1999 standard.</p>
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</blockquote>
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<div class="box"><em>End of informative text.</em></div>
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