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253 lines
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<title><complex.h></title>
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<basefont size="3"> <a name="<complex.h>"></a> <a name="tag_13_05"></a><!-- <complex.h> -->
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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_13_05_01"></a>NAME</h4>
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<blockquote>complex.h - complex arithmetic</blockquote>
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<h4><a name="tag_13_05_02"></a>SYNOPSIS</h4>
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<blockquote class="synopsis">
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<p><tt>#include <complex.h></tt></p>
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</blockquote>
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<h4><a name="tag_13_05_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>The <i><complex.h></i> header shall define the following macros:</p>
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<dl compact>
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<dt>complex</dt>
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<dd>Expands to <b>_Complex</b>.</dd>
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<dt>_Complex_I</dt>
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<dd>Expands to a constant expression of type <b>const float _Complex</b>, with the value of the imaginary unit (that is, a number
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<i>i</i> such that <i>i</i><small><sup>2</sup></small>=-1).</dd>
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<dt>imaginary</dt>
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<dd>Expands to <b>_Imaginary</b>.</dd>
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<dt>_Imaginary_I</dt>
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<dd>Expands to a constant expression of type <b>const float _Imaginary</b> with the value of the imaginary unit.</dd>
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<dt>I</dt>
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<dd>Expands to either _Imaginary_I or _Complex_I. If _Imaginary_I is not defined, I expands to _Complex_I.</dd>
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</dl>
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<p>The macros imaginary and _Imaginary_I shall be defined if and only if the implementation supports imaginary types.</p>
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<p>An application may undefine and then, perhaps, redefine the complex, imaginary, and I macros.</p>
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<p>The following shall be declared as functions and may also be defined as macros. Function prototypes shall be provided.</p>
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<pre>
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<tt>double cabs(double complex);
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float cabsf(float complex);
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long double cabsl(long double complex);
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double complex cacos(double complex);
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float complex cacosf(float complex);
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double complex cacosh(double complex);
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float complex cacoshf(float complex);
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long double complex cacoshl(long double complex);
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long double complex cacosl(long double complex);
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double carg(double complex);
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float cargf(float complex);
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long double cargl(long double complex);
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double complex casin(double complex);
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float complex casinf(float complex);
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double complex casinh(double complex);
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float complex casinhf(float complex);
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long double complex casinhl(long double complex);
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long double complex casinl(long double complex);
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double complex catan(double complex);
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float complex catanf(float complex);
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double complex catanh(double complex);
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float complex catanhf(float complex);
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long double complex catanhl(long double complex);
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long double complex catanl(long double complex);
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double complex ccos(double complex);
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float complex ccosf(float complex);
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double complex ccosh(double complex);
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float complex ccoshf(float complex);
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long double complex ccoshl(long double complex);
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long double complex ccosl(long double complex);
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double complex cexp(double complex);
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float complex cexpf(float complex);
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long double complex cexpl(long double complex);
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double cimag(double complex);
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float cimagf(float complex);
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long double cimagl(long double complex);
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double complex clog(double complex);
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float complex clogf(float complex);
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long double complex clogl(long double complex);
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double complex conj(double complex);
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float complex conjf(float complex);
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long double complex conjl(long double complex);
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double complex cpow(double complex, double complex);
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float complex cpowf(float complex, float complex);
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long double complex cpowl(long double complex, long double complex);
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double complex cproj(double complex);
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float complex cprojf(float complex);
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long double complex cprojl(long double complex);
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double creal(double complex);
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float crealf(float complex);
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long double creall(long double complex);
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double complex csin(double complex);
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float complex csinf(float complex);
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double complex csinh(double complex);
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float complex csinhf(float complex);
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long double complex csinhl(long double complex);
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long double complex csinl(long double complex);
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double complex csqrt(double complex);
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float complex csqrtf(float complex);
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long double complex csqrtl(long double complex);
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double complex ctan(double complex);
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float complex ctanf(float complex);
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double complex ctanh(double complex);
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float complex ctanhf(float complex);
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long double complex ctanhl(long double complex);
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long double complex ctanl(long double complex);
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</tt>
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</pre>
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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_13_05_04"></a>APPLICATION USAGE</h4>
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<blockquote>
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<p>Values are interpreted as radians, not degrees.</p>
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</blockquote>
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<h4><a name="tag_13_05_05"></a>RATIONALE</h4>
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<blockquote>
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<p>The choice of <i>I</i> instead of <i>i</i> for the imaginary unit concedes to the widespread use of the identifier <i>i</i> for
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other purposes. The application can use a different identifier, say <i>j</i>, for the imaginary unit by following the inclusion of
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the <i><complex.h></i> header with:</p>
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<pre>
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<tt>#undef I
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#define j _Imaginary_I
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</tt>
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</pre>
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<p>An <i>I</i> suffix to designate imaginary constants is not required, as multiplication by <i>I</i> provides a sufficiently
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convenient and more generally useful notation for imaginary terms. The corresponding real type for the imaginary unit is
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<b>float</b>, so that use of <i>I</i> for algorithmic or notational convenience will not result in widening types.</p>
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<p>On systems with imaginary types, the application has the ability to control whether use of the macro I introduces an imaginary
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type, by explicitly defining I to be _Imaginary_I or _Complex_I. Disallowing imaginary types is useful for some applications
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intended to run on implementations without support for such types.</p>
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<p>The macro _Imaginary_I provides a test for whether imaginary types are supported.</p>
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<p>The <i>cis</i>() function (<i>cos</i>(<i>x</i>) + <i>I</i>*<i>sin</i>(<i>x</i>)) was considered but rejected because its
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implementation is easy and straightforward, even though some implementations could compute sine and cosine more efficiently in
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tandem.</p>
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</blockquote>
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<h4><a name="tag_13_05_06"></a>FUTURE DIRECTIONS</h4>
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<blockquote>
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<p>The following function names and the same names suffixed with <i>f</i> or <i>l</i> are reserved for future use, and may be added
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to the declarations in the <i><complex.h></i> header.</p>
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<blockquote>
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<table cellpadding="3">
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<tr valign="top">
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<td align="left">
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<p class="tent"><br>
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<i>cerf</i>()<br>
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<i>cerfc</i>()<br>
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<i>cexp2</i>()<br>
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</p>
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</td>
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<td align="left">
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<p class="tent"><br>
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<i>cexpm1</i>()<br>
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<i>clog10</i>()<br>
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<i>clog1p</i>()<br>
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</p>
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</td>
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<td align="left">
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<p class="tent"><br>
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<i>clog2</i>()<br>
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<i>clgamma</i>()<br>
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<i>ctgamma</i>()<br>
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</p>
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</td>
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</tr>
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</table>
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</blockquote>
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</blockquote>
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<h4><a name="tag_13_05_07"></a>SEE ALSO</h4>
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<blockquote>
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<p>The System Interfaces volume of IEEE Std 1003.1-2001, <a href="../functions/cabs.html"><i>cabs</i>()</a>, <a href=
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"../functions/cacos.html"><i>cacos</i>()</a>, <a href="../functions/cacosh.html"><i>cacosh</i>()</a>, <a href=
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"../functions/carg.html"><i>carg</i>()</a>, <a href="../functions/casin.html"><i>casin</i>()</a>, <a href=
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"../functions/casinh.html"><i>casinh</i>()</a>, <a href="../functions/catan.html"><i>catan</i>()</a>, <a href=
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"../functions/catanh.html"><i>catanh</i>()</a>, <a href="../functions/ccos.html"><i>ccos</i>()</a>, <a href=
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"../functions/ccosh.html"><i>ccosh</i>()</a>, <a href="../functions/cexp.html"><i>cexp</i>()</a>, <a href=
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"../functions/cimag.html"><i>cimag</i>()</a>, <a href="../functions/clog.html"><i>clog</i>()</a>, <a href=
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"../functions/conj.html"><i>conj</i>()</a>, <a href="../functions/cpow.html"><i>cpow</i>()</a>, <a href=
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"../functions/cproj.html"><i>cproj</i>()</a>, <a href="../functions/creal.html"><i>creal</i>()</a>, <a href=
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"../functions/csin.html"><i>csin</i>()</a>, <a href="../functions/csinh.html"><i>csinh</i>()</a>, <a href=
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"../functions/csqrt.html"><i>csqrt</i>()</a>, <a href="../functions/ctan.html"><i>ctan</i>()</a>, <a href=
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"../functions/ctanh.html"><i>ctanh</i>()</a></p>
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</blockquote>
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<h4><a name="tag_13_05_08"></a>CHANGE HISTORY</h4>
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<blockquote>
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<p>First released in Issue 6. Included for alignment with 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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