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<h1 id="firstHeading" class="firstHeading">ccoshf, ccosh, ccoshl</h1> <table class="t-dcl-begin"> <tr class="t-dsc-header"> <th> Defined in header <code><complex.h></code> </th> <th> </th> <th> </th> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">float complex ccoshf( float complex z );</pre>
</td> <td> (1) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">double complex ccosh( double complex z );</pre>
</td> <td> (2) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">long double complex ccoshl( long double complex z );</pre>
</td> <td> (3) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> <tr class="t-dsc-header"> <th> Defined in header <code><tgmath.h></code> </th> <th> </th> <th> </th> </tr> <tr class="t-dcl t-since-c99"> <td> <pre data-language="c">#define cosh( z )</pre>
</td> <td> (4) </td> <td> <span class="t-mark-rev t-since-c99">(since C99)</span> </td> </tr> </table> <div class="t-li1">
<span class="t-li">1-3)</span> Computes the complex hyperbolic cosine of <code>z</code>.</div> <div class="t-li1">
<span class="t-li">4)</span> Type-generic macro: If <code>z</code> has type <code><span class="kw4">long</span> <span class="kw4">double</span> <a href="http://en.cppreference.com/w/c/numeric/complex/complex"><span class="kw743">complex</span></a></code>, <code>ccoshl</code> is called. if <code>z</code> has type <code><span class="kw4">double</span> <a href="http://en.cppreference.com/w/c/numeric/complex/complex"><span class="kw743">complex</span></a></code>, <code>ccosh</code> is called, if <code>z</code> has type <code><span class="kw4">float</span> <a href="http://en.cppreference.com/w/c/numeric/complex/complex"><span class="kw743">complex</span></a></code>, <code>ccoshf</code> is called. If <code>z</code> is real or integer, then the macro invokes the corresponding real function (<code>coshf</code>, <code><a href="http://en.cppreference.com/w/c/numeric/math/cosh"><span class="kw677">cosh</span></a></code>, <code>coshl</code>). If <code>z</code> is imaginary, then the macro invokes the corresponding real version of the function <code><a href="../math/cos" title="c/numeric/math/cos">cos</a></code>, implementing the formula cosh(iy) = cos(y), and the return type is real.</div> <h3 id="Parameters"> Parameters</h3> <table class="t-par-begin"> <tr class="t-par"> <td> z </td> <td> - </td> <td> complex argument </td>
</tr>
</table> <h3 id="Return_value"> Return value</h3> <p>If no errors occur, complex hyperbolic cosine of <code>z</code> is returned</p>
<h3 id="Error_handling_and_special_values"> Error handling and special values</h3> <p>Errors are reported consistent with <a href="../math/math_errhandling" title="c/numeric/math/math errhandling">math_errhandling</a></p>
<p>If the implementation supports IEEE floating-point arithmetic,</p>
<ul>
<li> <code>ccosh<span class="br0">(</span><a href="http://en.cppreference.com/w/c/numeric/complex/conj"><span class="kw760">conj</span></a><span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span> <span class="sy1">==</span> <a href="http://en.cppreference.com/w/c/numeric/complex/conj"><span class="kw760">conj</span></a><span class="br0">(</span>ccosh<span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span></code> </li>
<li> <code>ccosh(z) == ccosh(-z)</code> </li>
<li> If <code>z</code> is <code>+0+0i</code>, the result is <code>1+0i</code> </li>
<li> If <code>z</code> is <code>+0+∞i</code>, the result is <code>NaN±0i</code> (the sign of the imaginary part is unspecified) and <code><a href="../fenv/fe_exceptions" title="c/numeric/fenv/FE exceptions">FE_INVALID</a></code> is raised </li>
<li> If <code>z</code> is <code>+0+NaNi</code>, the result is <code>NaN±0i</code> (the sign of the imaginary part is unspecified) </li>
<li> If <code>z</code> is <code>x+∞i</code> (for any finite non-zero x), the result is <code>NaN+NaNi</code> and <code><a href="../fenv/fe_exceptions" title="c/numeric/fenv/FE exceptions">FE_INVALID</a></code> is raised </li>
<li> If <code>z</code> is <code>x+NaNi</code> (for any finite non-zero x), the result is <code>NaN+NaNi</code> and <code><a href="../fenv/fe_exceptions" title="c/numeric/fenv/FE exceptions">FE_INVALID</a></code> may be raised </li>
<li> If <code>z</code> is <code>+∞+0i</code>, the result is <code>+∞+0i</code> </li>
<li> If <code>z</code> is <code>+∞+yi</code> (for any finite non-zero y), the result is <code>+∞cis(y)</code> </li>
<li> If <code>z</code> is <code>+∞+∞i</code>, the result is <code>±∞+NaNi</code> (the sign of the real part is unspecified) and <code><a href="../fenv/fe_exceptions" title="c/numeric/fenv/FE exceptions">FE_INVALID</a></code> is raised </li>
<li> If <code>z</code> is <code>+∞+NaN</code>, the result is <code>+∞+NaN</code> </li>
<li> If <code>z</code> is <code>NaN+0i</code>, the result is <code>NaN±0i</code> (the sign of the imaginary part is unspecified) </li>
<li> If <code>z</code> is <code>NaN+yi</code> (for any finite non-zero y), the result is <code>NaN+NaNi</code> and <code><a href="../fenv/fe_exceptions" title="c/numeric/fenv/FE exceptions">FE_INVALID</a></code> may be raised </li>
<li> If <code>z</code> is <code>NaN+NaNi</code>, the result is <code>NaN+NaNi</code> </li>
</ul> <p>where cis(y) is cos(y) + i sin(y)</p>
<h3 id="Notes"> Notes</h3> Mathematical definition of hyperbolic cosine is cosh z = <span><span>ez+e-z</span><span>/</span><span>2</span></span> <p>Hyperbolic cosine is an entire function in the complex plane and has no branch cuts. It is periodic with respect to the imaginary component, with period 2πi</p>
<h3 id="Example"> Example</h3> <div class="t-example"> <div class="c source-c"><pre data-language="c">#include <stdio.h>
#include <math.h>
#include <complex.h>
int main(void)
{
double complex z = ccosh(1); // behaves like real cosh along the real line
printf("cosh(1+0i) = %f%+fi (cosh(1)=%f)\n", creal(z), cimag(z), cosh(1));
double complex z2 = ccosh(I); // behaves like real cosine along the imaginary line
printf("cosh(0+1i) = %f%+fi ( cos(1)=%f)\n", creal(z2), cimag(z2), cos(1));
}</pre></div> <p>Output:</p>
<div class="text source-text"><pre data-language="c">cosh(1+0i) = 1.543081+0.000000i (cosh(1)=1.543081)
cosh(0+1i) = 0.540302+0.000000i ( cos(1)=0.540302)</pre></div> </div> <h3 id="References"> References</h3> <ul>
<li> C11 standard (ISO/IEC 9899:2011): </li>
<ul>
<li> 7.3.6.4 The ccosh functions (p: 193) </li>
<li> 7.25 Type-generic math <tgmath.h> (p: 373-375) </li>
<li> G.6.2.4 The ccosh functions (p: 541) </li>
<li> G.7 Type-generic math <tgmath.h> (p: 545) </li>
</ul>
<li> C99 standard (ISO/IEC 9899:1999): </li>
<ul>
<li> 7.3.6.4 The ccosh functions (p: 175) </li>
<li> 7.22 Type-generic math <tgmath.h> (p: 335-337) </li>
<li> G.6.2.4 The ccosh functions (p: 476) </li>
<li> G.7 Type-generic math <tgmath.h> (p: 480) </li>
</ul>
</ul> <h3 id="See_also"> See also</h3> <table class="t-dsc-begin"> <tr class="t-dsc"> <td> <div><a href="csinh" title="c/numeric/complex/csinh"> <span class="t-lines"><span>csinh</span><span>csinhf</span><span>csinhl</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes the complex hyperbolic sine <br> <span class="t-mark">(function)</span> </td>
</tr> <tr class="t-dsc"> <td> <div><a href="ctanh" title="c/numeric/complex/ctanh"> <span class="t-lines"><span>ctanh</span><span>ctanhf</span><span>ctanhl</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes the complex hyperbolic tangent <br> <span class="t-mark">(function)</span> </td>
</tr> <tr class="t-dsc"> <td> <div><a href="cacosh" title="c/numeric/complex/cacosh"> <span class="t-lines"><span>cacosh</span><span>cacoshf</span><span>cacoshl</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes the complex arc hyperbolic cosine <br> <span class="t-mark">(function)</span> </td>
</tr> <tr class="t-dsc"> <td> <div><a href="../math/cosh" title="c/numeric/math/cosh"> <span class="t-lines"><span>cosh</span><span>coshf</span><span>coshl</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div> </td> <td> computes hyperbolic cosine (\({\small\cosh{x} }\)cosh(x)) <br> <span class="t-mark">(function)</span> </td>
</tr> <tr class="t-dsc"> <td colspan="2"> <span><a href="https://en.cppreference.com/w/cpp/numeric/complex/cosh" title="cpp/numeric/complex/cosh">C++ documentation</a></span> for <code>cosh</code> </td>
</tr> </table> <div class="_attribution">
<p class="_attribution-p">
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