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<h1 id="firstHeading" class="firstHeading">csqrtf, csqrt, csqrtl</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 csqrtf( 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 csqrt( 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 csqrtl( 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 sqrt( 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 square root of <code>z</code> with branch cut along the negative real axis.</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>csqrtl</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>csqrt</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>csqrtf</code> is called. If <code>z</code> is real or integer, then the macro invokes the corresponding real function (<code>sqrtf</code>, <code><a href="http://en.cppreference.com/w/c/numeric/math/sqrt"><span class="kw665">sqrt</span></a></code>, <code>sqrtl</code>). If <code>z</code> is imaginary, the corresponding complex number version is called.</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, returns the square root of <code>z</code>, in the range of the right half-plane, including the imaginary axis ([0; +∞) along the real axis and (−∞; +∞) along the imaginary axis.)</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> The function is continuous onto the branch cut taking into account the sign of imaginary part </li>
<li> <code>csqrt<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>csqrt<span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span></code> </li>
<li> If <code>z</code> is <code>±0+0i</code>, the result is <code>+0+0i</code> </li>
<li> If <code>z</code> is <code>x+∞i</code>, the result is <code>+∞+∞i</code> even if x is NaN </li>
<li> If <code>z</code> is <code>x+NaNi</code>, the result is <code>NaN+NaNi</code> (unless x is ±∞) 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>-∞+yi</code>, the result is <code>+0+∞i</code> for finite positive y </li>
<li> If <code>z</code> is <code>+∞+yi</code>, the result is <code>+∞+0i)</code> for finite positive y </li>
<li> If <code>z</code> is <code>-∞+NaNi</code>, the result is <code>NaN±∞i</code> (sign of imaginary part unspecified) </li>
<li> If <code>z</code> is <code>+∞+NaNi</code>, the result is <code>+∞+NaNi</code> </li>
<li> If <code>z</code> is <code>NaN+yi</code>, 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> <h3 id="Example"> Example</h3> <div class="t-example"> <div class="c source-c"><pre data-language="c">#include <stdio.h>
#include <complex.h>
int main(void)
{
double complex z1 = csqrt(-4);
printf("Square root of -4 is %.1f%+.1fi\n", creal(z1), cimag(z1));
double complex z2 = csqrt(conj(-4)); // or, in C11, CMPLX(-4, -0.0)
printf("Square root of -4-0i, the other side of the cut, is "
"%.1f%+.1fi\n", creal(z2), cimag(z2));
}</pre></div> <p>Output:</p>
<div class="text source-text"><pre data-language="c">Square root of -4 is 0.0+2.0i
Square root of -4-0i, the other side of the cut, is 0.0-2.0i</pre></div> </div> <h3 id="References"> References</h3> <ul>
<li> C11 standard (ISO/IEC 9899:2011): </li>
<ul>
<li> 7.3.8.3 The csqrt functions (p: 196) </li>
<li> 7.25 Type-generic math <tgmath.h> (p: 373-375) </li>
<li> G.6.4.2 The csqrt functions (p: 544) </li>
<li> G.7 Type-generic math <tgmath.h> (p: 545) </li>
</ul>
<li> C99 standard (ISO/IEC 9899:1999): </li>
<ul>
<li> 7.3.8.3 The csqrt functions (p: 178) </li>
<li> 7.22 Type-generic math <tgmath.h> (p: 335-337) </li>
<li> G.6.4.2 The csqrt functions (p: 479) </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="cpow" title="c/numeric/complex/cpow"> <span class="t-lines"><span>cpow</span><span>cpowf</span><span>cpowl</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 power function <br> <span class="t-mark">(function)</span> </td>
</tr> <tr class="t-dsc"> <td> <div><a href="../math/sqrt" title="c/numeric/math/sqrt"> <span class="t-lines"><span>sqrt</span><span>sqrtf</span><span>sqrtl</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 square root (\(\small{\sqrt{x} }\)<span class="t-mrad"><span>√</span><span>x</span></span>) <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/sqrt" title="cpp/numeric/complex/sqrt">C++ documentation</a></span> for <code>sqrt</code> </td>
</tr> </table> <div class="_attribution">
<p class="_attribution-p">
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